Garriga Valle, Ernest
Total activity: 71
Department
Department of Applied Mathematics IV
E-mail
egarrigama4.upc.edu
Contact details
UPC directory

## Scientific and technological production Ordered by:  Date asc. Date desc. Title asc. Title desc. Researcher asc. Researcher desc.

1 to 50 of 71 results
• Moments in graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Discrete applied mathematics
Date of publication: 2013
Journal article

This parameter generalizes, or it is closely related to, some well-known graph invariants, such as the Wiener index W (G), when rho(u) = 1/2 for every u is an element of V, and the degree distance D'(G), obtained when rho(u) = delta(u), the degree of vertex u. In this paper we derive some exact formulas for computing the rho-moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding rho-moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same rho-moment for every rho (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product.

Let G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where dist( ; ) stands for the distance function. Adding up all these numbers, we obtain the -moment of G: This parameter generalizes, or it is closely related to, some well-known graph invari- ants, such as the Wiener index W(G), when (u) = 1=2 for every u 2 V , and the degree distance D0(G), obtained when (u) = (u), the degree of vertex u. In this paper we derive some exact formulas for computing the -moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding -moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same -moment for every (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product.

Postprint (author’s final draft)

• 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; Garriga Valle, Ernest; 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; 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
Participation in a competitive project

• Edge distance-regular graphs

Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic notes in discrete mathematics
Date of publication: 2011
Journal article

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

* distance-regularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphs

• Dual concepts of almost distance-regularity and the spectral excess theorem

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Discrete mathematics
Date of publication: 2011
Journal article

• A differential approach for bounding the index of graphs under perturbations

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 2011-09-02
Journal article

This paper presents bounds for the variation of the spectral radius (G) of a graph G after some perturbations or local vertex/edge modifications of G. The perturbations considered here are the connection of a new vertex with, say, g vertices of G, the addition of a pendant edge (the previous case with g = 1) and the addition of an edge. The method proposed here is based on continuous perturbations and the study of their differential inequalities associated. Within rather economical information (namely, the degrees of the vertices involved in the perturbation), the best possible inequalities are obtained. In addition, the cases when equalities are attained are characterized. The asymptotic behavior of the bounds obtained is also discussed.

• Edge-distance-regular graphs

Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Journal of combinatorial theory. Series A
Date of publication: 2011
Journal article

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

• A differential approach for bounding the index of graphs under perturbations

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Date: 2011-03
Report

• Edge-distance-regular graphs

Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Date: 2011-03-11
Report

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edgedistance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.

• Edge-distance-regularity

Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
International Workshop on Network Topologies
Presentation's date: 2011-07-14
Presentation of work at congresses

• A new differencial approach to bound the spectral radius of graphs under perturbations

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Slovenian International Conference on Graph Theory
Presentation's date: 2011-06-21
Presentation of work at congresses

• Edge-distance-regular graphs

Cámara Vallejo, Marc; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
European Conference on Combinatorics, Graph Theory and Applications
Presentation's date: 2011-08-31
Presentation of work at congresses

• Combinatorial vs. Algebraic Characterizations of Completely Pseudo-Regular Codes

Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 2010-03-08
Journal article

• A simple proof of the spectral excess theorem for distance-regular graphs

Fiol Mora, Miquel Àngel; Gago Alvarez, Silvia; Garriga Valle, Ernest
Linear algebra and its applications
Date of publication: 2010-04-15
Journal article

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.

• Characterizing (l, m)-walk-regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Linear algebra and its applications
Date of publication: 2010-12-30
Journal article

• On almost distance-regular graphs

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Journal of combinatorial theory. Series A
Date of publication: 2010
Journal article

Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distanceregular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called m-walkregularity. Another studied concept is that of m-partial distanceregularity or, informally, distance-regularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of ( ,m)-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distanceregular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem.

• The geometry of t-spreads in k-walk-regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Journal of graph theory
Date of publication: 2010-08
Journal article

A graph is walk-regular if the number of closed walks of length rooted at a given vertex is a constant through all the vertices for all . For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D=d, we study the geometry of its d-spreads, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a simplex (or tetrahedron in a three-dimensional case) and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-spreads or vertices at distance t from each other.

• On Almost Distance-Regular Graphs

Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Date: 2010-03-12
Report

• Dual concepts of almost distance-regularity and the spectral excess theorem

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
International Workshop on Optimal Network Topologies
Presentation of work at congresses

• When almost distance-regularity attains distance-regularity

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
French Combinatorial Conference
Presentation's date: 2010-06-28
Presentation of work at congresses

Generally speaking, `almost distance-regular graphs' are graphs which share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we rst propose four basic di erent (but closely related) concepts of almost distance-regularity. In some cases, they coincide with concepts introduced before by other authors, such as walk-regular graphs and partially distance-regular graphs. Here it is always assumed that the diameter D of the graph attains its maximum possible value allowed by its number d+1 of di erent eigenvalues; that is, D = d, as happens in every distance-regular graph. Our study focuses on nding out when almost distance- regularity leads to distance-regularity. In other words, some `economic' (in the sense of minimizing the number of conditions) old and new characterizations of distance- regularity are discussed. For instance, if A0;A1; : : : ;AD and E0;E1; : : : ;Ed denote, respectively, the distance matrices and the idempotents of the graph; and D and A stand for their respective linear spans, any of the two following `dual' conditions su ce: (a) A0;A1;AD 2 A; (b) E0;E1;Ed 2 D. Moreover, other characterizations based on the preintersection parameters, the average intersection numbers and the recurrence coe cients are obtained. In some cases, our results can be also seen as a generalization of the so-called spectral excess theorem for distance-regular graphs.

• A taste of duality in almost distance-regularity

Fiol Mora, Miquel Àngel; Dalfo Simo, Cristina; Van Dam, Edwin R; Garriga Valle, Ernest
Swedish-Catalan Conference in Mathematics
Presentation's date: 2010-09-17
Presentation of work at congresses

• Local spectrum of the subconstituents and completely pseudo-regular codes

Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 2010-07-08
Presentation of work at congresses

• When almost distance regularity attains distance regularity

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
International Workshop on Optimal Network Topologies
Presentation's date: 2010-06-10
Presentation of work at congresses

• On almost distance-regular graphs

Dalfo Simo, Cristina; Van Dam, Edwin R; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bram
Joint Mathematical Conference CSASC
Presentation's date: 2010-01-25
Presentation of work at congresses

• On t-cliques in k-walk-regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
EUROCOMB'09: European Conference on Combinatorics, Graph Theory and Applicactions
Presentation's date: 2009-09-10
Presentation of work at congresses

A graph is walk-regular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a regular tetrahedron and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-cliques or vertices at distance t from each other.

• On k-walk-regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
British Combinatorial Conference
Presentation of work at congresses

• Number of walks and degree powers in a graph

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Discrete mathematics
Date of publication: 2009-04
Journal article

• On k-Walk-Regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 2009-04
Journal article

• Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes

Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic journal of combinatorics
Date of publication: 2009-07
Journal article

• On t-cliques in k-walk-regular graphs

Dalfo Simo, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic notes in discrete mathematics
Date of publication: 2009-08
Journal article

A graph is walk-regular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a regular tetrahedron and we compute its parameters. Moreover, the results are generalized to the case of k-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their t-cliques or vertices at distance t from each other.

• 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
Participation in a competitive project

• COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

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

• Algunas aplicaciones de polinomios ortogonales de variable discreta a grafos y códigos

Garriga Valle, Ernest
Seminario de Matemática Discreta
Presentation's date: 2008-09-09
Presentation of work at congresses

• Algunas aplicaciones de polinomios ortogonales de variable discreta a grafos y códigos

Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Seminario de Matemática Discreta
Presentation's date: 2008-09-09
Presentation of work at congresses

• Algunas aplicaciones de polinomios octogonales de variable discreta a grafos y códigos

Cámara Vallejo, Marc; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Jornadas de Matemática Discreta y Algorítmica
Presentation of work at congresses

• A new Approach to the Spectral Excess Theorem for Distance-Regular Graphs

Gago Alvarez, Silvia; Garriga Valle, Ernest; Fiol Mora, Miquel Àngel
Workshop on Spectral Graph Theory with applications on Computer Science, Combinatorial Optimization and Chemistry
Presentation's date: 2008-12-01
Presentation of work at congresses

The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph \$\Gamma\$ with \$d+1\$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The original approach, due to Fiol and Garriga in \$1997\$, was obtained in a wide context from a local point of view, so giving a characterization of the so-called pseudo-distance-regularity around a vertex.\ In this paper we present a new simple method based in a global point of view, and where the mean degree of the distance-\$d\$ graph \$\Gamma_d\$ plays an essential role.

• Spectral and Geometric Properties of k-Walk-Regular Graphs

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Electronic notes in discrete mathematics
Date of publication: 2007-08
Journal article

• Una experiencia docente orientada a incrementar el trabajo personal del estudiante

Otero Calviño, Beatriz; Martí Farré, Jaume; Garriga Valle, Ernest; Alonso Maleta, Maria Aranzazu; LLUIS, PRAT; Prat Viñas, Luis
Jornadas de Enseñanza Universitaria de la Informática
Presentation of work at congresses

• On outindependent subgraphs of strongly regular graphs

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Linear and multilinear algebra
Date of publication: 2006-03
Journal article

• On the spectrum of an extremal graph with four eigenvalues

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Discrete mathematics
Date of publication: 2006-09
Journal article

• Number of Walks and Degree Powers in a Graph*

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Date: 2006-04
Report

• Combinatòria, Teoria de Grafs i Aplicacions

Serra Albo, Oriol; Aguilo Gost, Francisco de Asis Luis; Andrés Yebra, José Luis; Balbuena Martinez, Maria Camino Teofila; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Marcote Ordax, Francisco Javier; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Moragas Vilarnau, Jordi; Montejano Cantoral, Amanda; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Zaragoza Monroig, Maria Luisa
Participation in a competitive project

• Avoiding monocoloured triangles when colouring Kn

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Andres Yebra, Jose Luis
Date: 2004-08
Report

• An algebraic characterization of completely regular codes in distance-regular graphs

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
SIAM journal on discrete mathematics
Date of publication: 2002-03
Journal article

• Pseudo-strong regularity around a set

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Linear and multilinear algebra
Date of publication: 2002-03
Journal article

• Aprenentatge de càlcul-1. successions, contiuïtat i derivació.

Aguilo Gost, Francisco de Asis Luis; Miralles De La Asuncion, Alicia; Garriga Valle, Ernest; Barguilla Navarrete, Jorge
Date of publication: 2002-09-30
Book

• Aprenentatge de Càlcul -2. Integració i sèries.

Aguilo Gost, Francisco de Asis Luis; Garriga Valle, Ernest; Miralles De La Asuncion, Alicia; Barguilla Navarrete, Jorge
Date of publication: 2002-09-30
Book

• Some algebraic characterization of completely regular and perfect codes

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
British Combinatorial Conference
Presentation of work at congresses

• Algebraic characterizations of completely regular codes

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
SIAM journal on discrete mathematics
Date of publication: 2001-10
Journal article

• Boundary graphs: The limit case of a spectral property

Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Andres Yebra, Jose Luis
Discrete mathematics
Date of publication: 2001-01
Journal article