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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.

  • 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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  • 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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  • Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

     Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Garriga Valle, Ernest; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
    Competitive project

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  • WORKSHOP ON GRAPH SPECTRA APPLICATIONS IN COMPUTER SCIENCE

     Fàbrega Canudas, Josep; Comellas Padro, Francesc de Paula; Stevanovic, Dragan; Mitjana Riera, Margarida; Dalfo Simo, Cristina
    Competitive project

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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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  • Weakly distance-regular digraphs revisited

     Mitjana Riera, Margarida
    International Workshop on Optimal Network Topologies
    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
    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.

  • 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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  • 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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  • INTERNATIONAL WORKSHOP ON OPTIMAL NETWORK TOPOLOGIES

     Serra Albo, Oriol; Fàbrega Canudas, Josep; Mitjana Riera, Margarida; Balbuena Martinez, Maria Camino Teofila; Comellas Padro, Francesc de Paula
    Competitive project

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  • The local spectra of regular line graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Discrete mathematics
    Vol. 310, num. 3, p. 511-517
    DOI: 10.1016/j.disc.2009.03.034
    Date of publication: 2010-02
    Journal article

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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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  • 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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  • Llibre blanc de la recerca matemàtica a Catalunya (2000-2009)

     Castellet Solanas, Manuel; del Castillo Franquet, Joan; Jarque Ribera, Xavier; Mitjana Riera, Margarida
    Date of publication: 2010-09
    Book

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  • 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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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     López Masip, Susana Clara; Cámara Vallejo, Marc; Moragas Vilarnau, Jordi; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Rius Font, Miquel; Espona Dones, Margarida; Garriga Valle, Ernest; Dalfo Simo, Cristina; Pérez Mansilla, Sonia; Miralles De La Asuncion, Alicia; Gomez Marti, Jose; Zaragoza Monroig, Maria Luisa; Muñoz Lopez, Francisco Javier; Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel; Fàbrega Canudas, Josep; Andres Yebra, Jose Luis; Barriere Figueroa, Eulalia; Llado Sanchez, Anna; Mitjana Riera, Margarida; Ball, Simeon Michael; Gago Alvarez, Silvia; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
    Competitive project

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  • PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

     Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
    Competitive project

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  • On the spectra of sequence graphs

     Mitjana Riera, Margarida; Fiol Mora, Miquel Àngel
    British Combinatorial Conference
    Presentation's date: 2009-07-06
    Presentation of work at congresses

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  • The generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Discrete mathematics
    Vol. 309, num. 12, p. 3871-3881
    Date of publication: 2009-06
    Journal article

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  • Algebraic properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Geometric and Algebraic Combinatorics 4
    p. 3
    Presentation's date: 2008-08
    Presentation of work at congresses

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  • New operations on graphs and digraphs. Algebraic properties

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    (SGT in Rio 08) Workshop on spectral graph theory with appl. on computer science, combinatorial optimization and chemistry
    Presentation's date: 2008-12
    Presentation of work at congresses

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  • Some properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 147-154
    Presentation's date: 2008-07
    Presentation of work at congresses

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  • On middle cube graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida; Dalfo Simo, Cristina; Barriere Figueroa, Eulalia
    SIAM Conference on Discrete Mathematics
    Presentation's date: 2008
    Presentation of work at congresses

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  • The spectra of Manhattan street networks

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 429, num. 7, p. 1823-1839
    Date of publication: 2008-10
    Journal article

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  • Algebraic properties of the generalized hierarchical product of graphs

     Barriere Figueroa, Eulalia; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 139-146
    Presentation's date: 2008-07
    Presentation of work at congresses

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  • The spectra of Manhattan networks

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    1st Canadian Discrete and Algorithmic Mathematics Conference
    Presentation of work at congresses

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  • A spectral study of the Manhattan networks

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    European Conference on Combinatorics, Graph Theory, and Applications
    p. 233-237
    Presentation's date: 2007-09-11
    Presentation of work at congresses

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  • The local spectra of line graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 28, num. --, p. 95-102
    Date of publication: 2007-03
    Journal article

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  • The spectra of some families of digraphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Linear algebra and its applications
    Vol. 423, num. 1, p. 109-118
    DOI: 10.1016/j.laa.2006.11.018
    Date of publication: 2007-05
    Journal article

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  • A spectral study of the Manhattan networks

     Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Electronic notes in discrete mathematics
    Vol. 29, num. 1, p. 267-271
    Date of publication: 2007-08
    Journal article

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  • The spectra of some families of digraphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Aveiro Workshop on Graph Spectra
    p. 26
    Presentation of work at congresses

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  • The local spectra of line graphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Sixth Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications
    p. 89
    Presentation of work at congresses

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  • Aproximación geométrica al espectro de algunas familias de digrafos

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Jornadas de Matemática Discreta y Algorítmica
    p. 287-295
    Presentation's date: 2006-07-13
    Presentation of work at congresses

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  • Geometric approximation of the spectrum of some families of digraphs

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Date of publication: 2006-07
    Book chapter

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  • The Local Spectra of Regular Line Graphs*

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Date: 2006-10
    Report

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  • The Spectra of Some Families of Digraphs*

     Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
    Date: 2006-08
    Report

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  • On the weak distance-regularity of Moore-type digraphs

     Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel; Gimbert, J; Mitjana Riera, Margarida
    Linear and multilinear algebra
    Vol. 54, num. 4, p. 265-284
    DOI: 10.1080/03081080500423825
    Date of publication: 2006-07
    Journal article

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