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  • Potential Theory on finite networks

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 46, p. 113-120
    DOI: 10.1016/j.endm.2014.08.016
    Date of publication: 2014-09-16
    Journal article

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    We survey here some techniques from Potential Theory and show their use in electrical networks. We are focused on the linear aspect of the theory; that is, on the analysis of singular an positive semidefinite Schrödinger operators and we show the relation between this class of operators and singular M-matrices, paying attention on the properties of superharmonic functions. We also apply these methods to establish some global results on the associated Markov chains

  • Discrete elliptic operators and their Green operators

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 442, p. 115-134
    Date of publication: 2014
    Journal article

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  • Laplacian matrix of a weighted graph with new pendant vertices

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 46, p. 129-136
    DOI: 10.1016/j.endm.2014.08.018
    Date of publication: 2014-09
    Journal article

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    The Laplacian matrix of a simple graph has been widely studied, as a consequence of its applications. However the Laplacian matrix of a weighted graph is still a challenge. In this work we provide the Moore-Penrose inverse of the Laplacian matrix of the graph obtained adding new pendant vertices to an initial graph, in terms of the Moore-Penrose inverse of the Laplacian matrix of the original graph. As an application we can compute the effective resistances and the Kirchhoff index of the new network.

  • The Kirchhoff index of unicycle weighted chains

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 46, p. 217-224
    DOI: 10.1016/j.endm.2014.08.029
    Date of publication: 2014-09-16
    Journal article

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    We consider a class of generalized linear chains, namely, the unicycle chains as a perturbation of a 2nâ¿¿path by adding one weighted edge between two specific vertices. This class of chains includes, in particular, the weighted cycle. In this work, we obtain the Green function, the effective resistance and the Kirchhoff index of the unicycle chains as a function of the Green function, the effective resistance and the Kirchhoff index of a path, respectively.

  • The Inverse Problem on Finite Networks

     Arauz Lombardia, Cristina
    Universitat Politècnica de Catalunya
    Theses

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    Aquesta tesi té dos objectius generals. Primer, volem deduir dades funcionals, estructurals o resistives d'una xarxa fent servir la informació proporcionada per la seva conductivitat. L'objectiu real és aconseguir aquesta informació d'una xarxa gran quan coneixem la mateixa de les subxarxes que la formen. El motiu és que les xarxes grans no són fàcils de treballar a causa de la seva mida. Com més petita sigui una xarxa, més fàcil serà treballar-hi, i per tant intentem trencar les xarxes grans en parts més petites que potser ens permeten resoldre problemes sobre elles més fàcilment. Principalment busquem les expressions de certs operadors que caracteritzen les solucions dels problemes de contorn en les xaxes originals. Aquests problemes es diuen problemes directes, ja que s'empren directament les dades de conductivitat per obtenir informació.El segon objectiu és recuperar les dades de conductivitat a l'interior d'una xarxa emprant només mesures a la frontera de la mateixa i condicions d'equiliri globals. Com que aquest problema no està ben establert perquè és altament sensible als canvis en les dades de frontera, de vegades només busquem una reconstrucció partial de la conductivitat o afegim condicions a la xarxa per tal de recuperar completament la conductivitat. Aquest tipus de problemes es diuen problemes inversos, ja que es fa servir informació a la frontera per aconseguir coneixements de l'interior de la xarxa. Aquest treball tracta de trobar situacions on la recuperació, total o parcial, es pugui dur a terme.Una de les nostres ambicions quant a problemes inversos és recuperar l'estructura de les xarxes per les que el ben conegut Problema de Serrin té solució en el camp discret. Sorprenentment, la resposta és similar al cas continu. També volem caracteritzar les xarxes mitjançant un operador a la frontera. Amb aquesta finalitat definim els problemes de contorn parcials sobredeterminats i describim com les solucions d'aquesta família de problemes que tenen una propietat d'alternància a una part de la frontera es propaguen a través de la xarxa mantenint aquesta alternància. Si ens centrem en una certa família de xarxes, veiem que l'operador a la frontera que abans hem mencionat pot ser la matriu de respostes d'una família infinita de xarxes amb diferentes conductivitats. Escollint una extensió en concret, obtenim una única xarxa per la qual una matriu donada és la seva matriu de respostes.Un cop hem caracteritzat aquelles matrius que són la matriu de respostes de certes xarxes, intentem recuperar les conductàncies d'aquestes xarxes. Amb aquesta finalitat, caracteritzem qualsevol solució d'un problema de contorn parcial sobredeterminat. Després, analitzem dos gran grups de xarxes que tene propietats de frontera notables i que ens porten a la recuperació de les conductàncies de certes branques a prop de la frontera. L'objectiu és donar fórmules explícites per obtenir aquestes conductàncies. Fent servir aquestes fórmules, aconseguim dur a terme una recuperació completa de conductàncies sota certes circumstàncies.

  • On the M-matrix inverse problem for singular and symmetric Jacobi matrices

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Electronic Journal of Linear Algebra
    Vol. 24, p. 237-254
    Date of publication: 2013-01
    Journal article

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  • Boundary value problems for Schrödinger operators on a Path Associated to Orthogonal Polynomials

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    DOI: 10.1007/978-1-4614-7333-6
    Date of publication: 2013
    Book chapter

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    In this work we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights are determined by the coefficients of the three-term recurrence relation.

    In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights are determined by the coefficients of the three-term recurrence relation.

  • Special Matrices

     Carmona Mejias, Angeles
    Collaboration in journals

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  • El problema de Serrin discreto

     Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Congreso de Jóvenes Investigadores Real Sociedad Matemática Española
    p. 94
    Presentation's date: 2013-09-16
    Presentation of work at congresses

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    J. Serrin dio solución, en 1971, al siguiente problema de la Teoría del Potencial: sea O un dominio regular abierto, conexo y acotado del espacio Euclídeo tal que la solución u del problema de Dirichlet -¿u = 1 en O y u = 0 en d(O) viene sobredeterminada por la condición de que ¿u es constante en la frontera d(O). Entonces, O es una bola y u tiene simetría radial. Aquí consideramos el problema discreto análogo. Dado un grafo G = (V, E) y un subconjunto conexo F ¿ V, la solución del problema de Dirichlet L(u) = 1 en F y u = 0 en d(F ) se llama medida de equilibrio. El Problema de Serrin Discreto se formula como: ¿la condición adicional ¿u = constante en d(F) implica que F es una bola y u es radial? La respuesta es negativa. Imponiendo una restricción que demostramos necesaria, los valores de la medida de equilibrio sí que dependen de la distancia a la frontera y esto nos lleva a dar una caracterización de los grafos donde el Problema de Serrin Discreto tiene solución.

  • Green matrices associated with generalized linear polyominoes

     Mitjana Riera, Margarida; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Conference of the International Linear Algebra Society
    p. 80
    Presentation's date: 2013-06
    Presentation of work at congresses

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    A Polyomino is an edge¿conected union of cells in the planar square lattice. Polyominoes are very popular in mathematical recreations, and have found interest among mathematicians, physicists, biologists, and computer scientists as well. Because the chemical constitution of a molecule is conventionally represented by a molecular graph or network, the polyominoes have deserved the attention of the Organic Chemistry community. So, several molecular structure descriptors based in network structural descriptors, have been introduced. In particular, in the last decade a great amount of works devoted to calculate the Kirchhoff Index of linear polyominoes¿like networks, have been published. In this work we deal with this class of polyominoes, that we call generalized linear polyominoes, that besides the most popular class of linear polyomino chains, also includes cycles, Phenylenes and Hexagonal chains to name only a few. Because the Kirchhoff Index is the trace of the Green function of the network, here we obtain the Green function of generalized linear Polyominoes. To do this, we understand a Polyomino as a perturbation of a path by adding weighted edges between opposite vertices. Therefore, unlike the techniques used by Yang and Zhang in 2008, that are based on the decomposition of the combinatorial Laplacian in structured blocks, here we obtain the Green function of a linear Polyomino from a perturbation of the combinatorial Laplacian. This approach deeply link linear Polyomino Green functions with the inverse M ¿matrix problem and specially, with the so¿called Green matrices, of Gantmacher and Krein (1941).

  • Perturbations of Discrete Elliptic operators

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Conference of the International Linear Algebra Society
    p. 80-81
    Presentation's date: 2013-06
    Presentation of work at congresses

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  • Discrete Serrin's problem

     Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Conference of the International Linear Algebra Society
    p. 79-80
    Presentation's date: 2013-06
    Presentation of work at congresses

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    In 1971, J. Serrin solved the following problem on Potential Theory: If is a smooth bounded open connected domain in the Euclidean space for which the solution u to the Dirichlet problem u = -1 in and u = 0 on ¿ has overdetermined boundary condition ¿u ¿n = constant on ¿ , then is a ball and u has radial symmetry. This result has multiple extensions, and what is more interesting, the methods used for solving the problem have applications to study the symmetry of the solutions of very general elliptic problems. We consider here the discrete analogue problem. Specifically, given ¿ = (V,E) a graph and F ¿ V a connected subset, the solution of the Dirichlet problem L(u) = 1 on F and u = 0 on d(F) is known as equilibrium measure. Therefore, the discrete Serrin¿s problem can be formulated as: does the additional condition ¿u ¿n = constant on d(F) imply that F is a ball and u is radial? We provide some examples showing that the answer is negative. However, the values of the equilibrium measure depend on the distance to the boundary and hence we wonder if imposing some symmetries on the domain, the solution to Serrin¿s problem is radial. The conclusion is true for many families of graph with high degree of symmetry, for instance for distance¿regular graphs or spider networks.

  • Tree forest metrics for Schrödinger operators in networks

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications
    p. 27
    Presentation's date: 2013-07-12
    Presentation of work at congresses

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    Metrics in graphs provide measures of proximity between vertices. The classical short-path distances can be replaced for more general metrics, as the adjusted forest metric introduced by Chebotarev et al. in [2]. Other related distance is the one provided for the resistance distance of a network [3]. The objective of our work is to generalize the adjusted forest metric related to Laplacian operators to the adjusted forest metric related to Schr¨odinger operators, under the functional analysis framework. Furthermore, we show that it can be computed in terms ofthe effective resistances of the network.

  • Boundary value problems on a weighted path

     Gago Alvarez, Silvia; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Midsummer Combinatorial Workshop
    Presentation's date: 2013-08-01
    Presentation of work at congresses

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    In this work we solve usual boundary value problems on a weighted path via orthogonal polynomials

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    Boundary value problems for Schrödinger operators on a path  Open access

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Date: 2012-05-25
    Report

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    In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations.

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    Jacobi matrices and boundary value problems in distance-regular graphs  Open access

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Date: 2012-01-25
    Report

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    In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs.

  • The Kirchhoff indices of join networks

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Discrete applied mathematics
    Vol. 160, num. 1-2, p. 24-37
    DOI: 10.1016/j.dam.2011.09.017
    Date of publication: 2012-01
    Journal article

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  • The M-matrix inverse problem for singular and symmetric Jacobi matrices

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 436, num. 5, p. 1090-1098
    DOI: 10.1016/j.laa.2011.06.044
    Date of publication: 2012-03-01
    Journal article

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  • Distance-regular graphs having the M-property

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Linear and multilinear algebra
    Vol. 60, num. 2, p. 225-240
    DOI: 10.1080/03081087.2011.589047
    Date of publication: 2012-01-16
    Journal article

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  • Jacobi matrices and boundary value problems in distance-regular graphs

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Electronic journal of linear algebra
    Vol. 24, p. 202-2014
    Date of publication: 2012-11
    Journal article

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    Regular boundary value problems on a distance-regular graph associated with Schrodinger operators are analyzed. These problems include the cases in which the boundary has one or two vertices. In each case, the Green matrices are given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graphs.

  • Partial boundary value problems on finite networks

     Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    De Brún Workshop
    Presentation's date: 2012-12-05
    Presentation of work at congresses

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    Inverse boundary-value problems were born to answer the question of whether it is possible to determine the conductivity of a body by means of boundary measurements. These problems are exponentially ill-posed since its solutions are highly sensitive to changes in the boundary data. We are mainly interested on the discrete version of the problem, that is, the inverse boundary-value problems on finite weighted networks. The aim here is to study partial inverse boundary-value problems, which are characterized by the existence of a part of the boundary where no data is known. Given a weighted network with conductances on the edges $\Gamma=(V,c)$, we fix a proper and connected subset $F\subset V$ and will consider a certain kind of boundary value problems in which the values of the functions and of their normal derivatives are known at the same part of the boundary of $F$ and there exists another part of the boundary where no data is known. We determine when there is existance and/or uniqueness of solution on $\bar F$. For, it is mandatory to consider the Dirichlet-to-Neumann map of the network, its kernel and a local inverse of the matrix given by this kernel. We also observe that the kernel of the Dirichlet-to-Neumann map is a Schur Complement of the Schrödinger operator of the network.

  • Boundary value problems in distance-regular graphs

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    International Workshop on Optimal Network Topologies
    p. 16-17
    Presentation's date: 2012-07-28
    Presentation of work at congresses

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  • Generalized linear polyominoes, Green functions and Green matrices

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 151-158
    Presentation's date: 2012-07-13
    Presentation of work at congresses

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  • Perturbing networks

     Mitjana Riera, Margarida; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Latin Ibero-American Spectral Graph Theory Workshop
    p. 1
    Presentation's date: 2012-09-28
    Presentation of work at congresses

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  • Potential theory for perturbed Laplacian of finite networks

     Mitjana Riera, Margarida; Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    SIAM Conference on Applied Linear Algebra
    p. 111
    Presentation's date: 2012-06-22
    Presentation of work at congresses

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  • On the Moore-Penrose inverse of singular, symmetric and periodic Jacobi M-matrices

     Encinas Bachiller, Andres Marcos; Bendito Perez, Enrique; Carmona Mejias, Angeles; Mitjana Riera, Margarida
    SIAM Conference on Applied Linear Algebra
    Presentation's date: 2012-06-18
    Presentation of work at congresses

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  • Access to the full text
    Two-side boundary value problems in distance-regular graphs  Open access

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Jornadas de Matemática Discreta y Algorítmica
    p. 167-174
    Presentation's date: 2012-07-13
    Presentation of work at congresses

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    In this work we analyze regular boundary value problems on a distanceregular graph associated with Schr¨odinger operators in the case that the boundary has two vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrix is given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graph.

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    The Green function of a perturbed network  Open access

     Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 237-244
    Presentation's date: 2012-07
    Presentation of work at congresses

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    The díscrete Green functions and their relationship whit discrete Laplace equations have deserved the interest of many researchs useing different approac. In this work we derive the Green function of a perturbed network in terms of the Green function of its base network.

  • Green function on product networks

     Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Jornadas de Matemática Discreta y Algorítmica
    p. 159-166
    Presentation's date: 2012-07-12
    Presentation of work at congresses

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    Our objective is to determine the Green function of product networks in terms of the Green function of one of the factor networks and the eigenvalues and eigenfunctions of the Schr ¨odinger operator of the other factor network, which we consider that are known. Moreover, we use these results to obtain the Green function of spider networks in terms of Green functions over cicles and paths

    Our objective is to determine the Green function of product networks in terms of the Green function of one of the factor networks and the eigenvalues and eigenfunctions of the Schr odinger operator of the other factor network, which we consider that are known. Moreover, we use these results to obtain the Green function of spider networks in terms of Green functions over cicles and paths.

  • Problemas de contorno discretos y técnicas de aproximación en estados de equilibrio

     Arauz Lombardia, Cristina; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia; Medina Sierra, Agustin; Bendito Perez, Enrique
    Competitive project

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  • The Kirchhoff index of cluster networks

     Arauz Lombardia, Cristina; Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Electronic notes in discrete mathematics
    Vol. 38, p. 57-62
    DOI: 10.1016/j.endm.2011.09.010
    Date of publication: 2011-12-01
    Journal article

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  • On the moore-penrose inverse of distance-regular graphs

     Carmona Mejias, Angeles; Bendito Perez, Enrique; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 38, p. 227-232
    DOI: 10.1016/j.endm.2011.09.038
    Date of publication: 2011-12-01
    Journal article

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  • The Kirchhoff index of cluster networks

     Arauz Lombardia, Cristina; Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    European Conference on Combinatorics, Graph Theory and Applications
    p. 57-62
    DOI: 10.1016/j.endm.2011.09.010
    Presentation's date: 2011-08-30
    Presentation of work at congresses

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    In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff Index. During the last decade these parametres have been applied in Organic Chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules which have similar structural behaviours. Moreover, a wide range of generalized Kirchhoff Indexes for some networks have been introduced. The objective of the present work is to obtain the Kirchhoff Index for a wide range of composite networks known as cluster networks.

  • Jacobi matrices and boundary value problems in distance- regular graphs

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gago Alvarez, Silvia
    Directions in Matrix Theory
    p. 32
    Presentation's date: 2011-07-09
    Presentation of work at congresses

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  • On the M-matrix inverse problem for symmetric singular Jacobi matrices

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Directions in Matrix Theory
    p. 21
    Presentation's date: 2011-07
    Presentation of work at congresses

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  • The M-property for distance-regular graphs

     Mitjana Riera, Margarida; Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Linear Algebraic Techniques in Combinatorics/Graph Theory
    p. 6
    Presentation's date: 2011-02-02
    Presentation of work at congresses

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  • Problema 168

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    La Gaceta de la Real Sociedad Matemática Española
    Vol. 13, num. 4, p. 714
    Date of publication: 2010
    Journal article

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  • Eigenvalues, eigenfunctions and green's functions on a path via chebyshev polynomials

     Bendito Perez, Enrique; Encinas Bachiller, Andres Marcos; Carmona Mejias, Angeles
    Applicable analysis and discrete mathematics
    Vol. 3, num. 2, p. 282-302
    DOI: 10.2298/AADM0902282B
    Date of publication: 2010-10
    Journal article

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  • Kirchhoff indexes of a network

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 432, num. 9, p. 2278-2292
    DOI: 10.1016/j.laa.2009.05.032
    Date of publication: 2010-04-15
    Journal article

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    In this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with symmetries, specifically for weighted wagon-wheels and circular ladders.

  • Generalized inverses of symmetric M-matrices

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 432, num. 9, p. 2438-2454
    DOI: 10.1016/j.laa.2009.11.008
    Date of publication: 2010-04-15
    Journal article

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  • Access to the full text
    La función de Green y el índice de Kirchhoff de redes cluster  Open access

     Arauz Lombardia, Cristina; Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos
    Congress on Discrete Mathematics and Algorithms
    p. 79-88
    Presentation's date: 2010-07-09
    Presentation of work at congresses

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    En este trabajo determinamos las Funciones de Green, respecto de un peso fijado sobre los vértices, en una amplia clase de redes compuestas que se engloban bajo la denominación de redes cluster. También aplicamos las expresiones obtenidas al célculo de la resistencia efectiva, respecto de un peso, entre cualquier par de vértices y el índice de Kirchhoff de la red cluster, en términos de los parámetros correspondientes a cada uno de sus factores. Finalmente mostramos que la particularización de nuestros resultados al caso estándar, esto es, al caso de grafos con peso constante en los vértices, recupera las expresiones obtenidas por otros autores en trabajos previos.

    En este trabajo determinamos las Funciones de Green, respecto de un peso fijado sobre los vértices, en una amplia clase de redes compuestas que se engloban bajo la denominación de redes cluster. También aplicamos las expresiones obtenidas al cálculo de la resistencia efectiva, respecto de un peso, entre cualquier par de vértices y el Índice de Kirchhoff de la red cluster, en términos de los parámetros correspondientes a cada uno de sus factores. Finalmente mostramos que la particularización de nuestros resultados al caso estándar, esto es, al caso de grafos con peso constante en los vértices recupera las expresiones obtenidas por otros autores en trabajos previos.

  • M-Matrix Inverse problem for distance-regular graphs

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    International Workshop on Optimal Network Topologies
    p. 55-60
    Presentation's date: 2010-06-09
    Presentation of work at congresses

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  • The M¿matrix Moore¿Penrose inverse problem for weighted paths

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 41-42
    Presentation's date: 2010-07-08
    Presentation of work at congresses

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  • Projecte d¿ajut de suport als grus de recerca(SGR2009). Ref: SGR-00987(GRC).

     Carmona Mejias, Angeles; Bendito Perez, Enrique; Encinas Bachiller, Andres Marcos; Medina Sierra, Agustin
    Competitive project

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  • Characterization of symmetric M-matrices as resistive inverses

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel
    Linear algebra and its applications
    Vol. 430, num. 4, p. 1336-1349
    DOI: 10.1016/j.laa.2008.10.027
    Date of publication: 2009-02
    Journal article

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  • Computational cost of the Fekete problem I: The Forces Method on the 2-sphere

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel; Gómez, A.; Mouriño, C.; Sánchez, M. T.
    Journal of computational physics
    Vol. 228, num. 9, p. 3288-3306
    DOI: 10.1016/j.jcp.2009.01.021
    Date of publication: 2009-05
    Journal article

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  • A Formula for the Kirchhoff Index

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel
    SIAM Conference on Discrete Mathematics
    p. 34
    Presentation of work at congresses

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  • La cohomología de una red finita

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel
    Jornadas de Matemática Discreta y Algorítmica
    p. 163-170
    Presentation of work at congresses

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  • El índice de Kirchhoff y la capacidad de Wiener de una red

     Bendito Perez, Enrique; Carmona Mejias, Angeles; Encinas Bachiller, Andres Marcos; Gesto Beiroa, Jose Manuel
    Jornadas de Matemática Discreta y Algorítmica
    p. 155-162
    Presentation of work at congresses

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  • On the generalized inverses of symmetric M-matrices

     Carmona Mejias, Angeles
    (SGT in Rio 08) Workshop on spectral graph theory with appl. on computer science, combinatorial optimization and chemistry
    Presentation's date: 2008-12-03
    Presentation of work at congresses

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