COMBGRAF  Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
20170227T23:08:25Z

Classifing stars: a comparison between clasical, genetic and neural network algorithms
http://hdl.handle.net/2117/100683
Classifing stars: a comparison between clasical, genetic and neural network algorithms
Hernández Pajares, Manuel; Comellas Padró, Francesc de Paula; Monte Moreno, Enrique
20170208T13:26:04Z
Hernández Pajares, Manuel
Comellas Padró, Francesc de Paula
Monte Moreno, Enrique

Some spectral and quasispectral characterizations of distanceregular graphs
http://hdl.handle.net/2117/100654
Some spectral and quasispectral characterizations of distanceregular graphs
Abiad, Aida; Van Dam, Edwin R; Fiol Mora, Miquel Àngel
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distanceregular graph. By using the preintersection numbers we give some new spectral and quasispectral characterizations of distanceregularity, in particular for graphs with large girth or large oddgirth. (C) 2016 Published by Elsevier Inc.
© <2016>. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20170208T08:23:34Z
Abiad, Aida
Van Dam, Edwin R
Fiol Mora, Miquel Àngel
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distanceregular graph. By using the preintersection numbers we give some new spectral and quasispectral characterizations of distanceregularity, in particular for graphs with large girth or large oddgirth. (C) 2016 Published by Elsevier Inc.

The spectral excess theorem for distanceregular graphs having distanced graph with fewer distinct eigenvalues
http://hdl.handle.net/2117/100474
The spectral excess theorem for distanceregular graphs having distanced graph with fewer distinct eigenvalues
Fiol Mora, Miquel Àngel
Let Gamma be a distanceregular graph with diameter d and Kneser graph K = Gamma(d), the distanced graph of Gamma. We say that Gamma is partially antipodal when K has fewer distinct eigenvalues than Gamma. In particular, this is the case of antipodal distanceregular graphs (K with only two distinct eigenvalues) and the socalled halfantipodal distanceregular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distanceregular graphs (among regular graphs with d + 1 distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the socalled spectral excess theorem, which allows us to characterize those distanceregular graphs which are halfantipodal, antipodal, bipartite, or with Kneser graph being strongly regular.
The final publication is available at Springer via http://dx.doi.org/10.1007/s1080101506546
20170202T09:38:37Z
Fiol Mora, Miquel Àngel
Let Gamma be a distanceregular graph with diameter d and Kneser graph K = Gamma(d), the distanced graph of Gamma. We say that Gamma is partially antipodal when K has fewer distinct eigenvalues than Gamma. In particular, this is the case of antipodal distanceregular graphs (K with only two distinct eigenvalues) and the socalled halfantipodal distanceregular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distanceregular graphs (among regular graphs with d + 1 distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the socalled spectral excess theorem, which allows us to characterize those distanceregular graphs which are halfantipodal, antipodal, bipartite, or with Kneser graph being strongly regular.

Fast calculation of entropy with Zhang's estimator
http://hdl.handle.net/2117/100157
Fast calculation of entropy with Zhang's estimator
Lozano Bojados, Antoni; Casas Fernández, Bernardino; Bentz, Chris; Ferrer Cancho, Ramon
Entropy is a fundamental property of a repertoire. Here, we present an efficient algorithm to estimate the entropy of types with the help of Zhang’s estimator. The algorithm takes advantage of the fact that the number of different frequencies in a text is in general much smaller than the number of types. We justify the convenience of the algorithm by means of an analysis of the statistical properties of texts from more than 1000 languages. Our work opens up various possibilities for future research.
20170127T08:06:04Z
Lozano Bojados, Antoni
Casas Fernández, Bernardino
Bentz, Chris
Ferrer Cancho, Ramon
Entropy is a fundamental property of a repertoire. Here, we present an efficient algorithm to estimate the entropy of types with the help of Zhang’s estimator. The algorithm takes advantage of the fact that the number of different frequencies in a text is in general much smaller than the number of types. We justify the convenience of the algorithm by means of an analysis of the statistical properties of texts from more than 1000 languages. Our work opens up various possibilities for future research.

Symmetry breaking in tournaments
http://hdl.handle.net/2117/100103
Symmetry breaking in tournaments
Lozano Bojados, Antoni
We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices S in V(T) is a determining set for a tournament T if every nontrivial automorphism of T moves at least one vertex of S, while S is a resolving set for T if every two distinct vertices in T have different distances to some vertex in S. We show that the minimum size of a determining set for an order n tournament (its determining number) is bounded by n/3, while the minimum size of a resolving set for an order n strong tournament (its metric dimension) is bounded by n/2. Both bounds are optimal.
20170126T11:47:32Z
Lozano Bojados, Antoni
We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices S in V(T) is a determining set for a tournament T if every nontrivial automorphism of T moves at least one vertex of S, while S is a resolving set for T if every two distinct vertices in T have different distances to some vertex in S. We show that the minimum size of a determining set for an order n tournament (its determining number) is bounded by n/3, while the minimum size of a resolving set for an order n strong tournament (its metric dimension) is bounded by n/2. Both bounds are optimal.

Abelian Cayley digraphs with asymptotically large order for any given degree
http://hdl.handle.net/2117/99392
Abelian Cayley digraphs with asymptotically large order for any given degree
Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia
Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known large dense results were all nonconstructive.
20170117T08:34:07Z
Aguiló Gost, Francisco de Asis L.
Fiol Mora, Miquel Àngel
Pérez Mansilla, Sonia
Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known large dense results were all nonconstructive.

Sequence mixed graphs
http://hdl.handle.net/2117/98676
Sequence mixed graphs
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López, Nacho
A mixed graph can be seen as a type of digraph containing some edges (or two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and literated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the degree/diameter problem. Thus, our generalized approach gives rise to graphs that have also good ratio order/diameter. Moreover, we propose a general method for obtaining a sequence mixed diagraph by identifying some vertices of certain iterated line digraph. As a consequence, some results about distancerelated parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.
20161221T08:37:00Z
Dalfó Simó, Cristina
Fiol Mora, Miquel Àngel
López, Nacho
A mixed graph can be seen as a type of digraph containing some edges (or two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and literated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the degree/diameter problem. Thus, our generalized approach gives rise to graphs that have also good ratio order/diameter. Moreover, we propose a general method for obtaining a sequence mixed diagraph by identifying some vertices of certain iterated line digraph. As a consequence, some results about distancerelated parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.

Connected and internal graph searching
http://hdl.handle.net/2117/97422
Connected and internal graph searching
Barrière Figueroa, Eulalia; Fraigniaud, Pierre; Santoro, Nicola; Thilikos Touloupas, Dimitrios
This paper is concerned with the graph searching game. The search number es(G) of a graph G is the smallest number of searchers required to clear G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the connected version and of the monotone internal version of the graph searching problem comes from the fact that, as shown in the paper, none of these problems is minor closed for arbitrary graphs, as opposed to all known variants of the graph searching problem. Motivated by the fact that connected graph searching, and monotone internal graph searching are both minor closed in trees, we provide a complete characterization of the set of trees that can be cleared by a given number of searchers. In fact, we show that, in trees, there is only one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. This allows us to prove that, for any tree T, mis(T)= cs(T). For arbitrary graphs, we prove that there is a unique chain of inequalities linking all the search numbers above. More precisely, for any graph G, es(G)= is(G)= ms(G)leq mis(G)leq cs(G)= ics(G)leq mcs(G)=mics(G). The first two inequalities can be strict. In the case of trees, we have mics(G)leq 2 es(T)2, that is there are exactly 2 different search numbers in trees, and these search numbers differ by a factor of 2 at most.
20161129T13:30:39Z
Barrière Figueroa, Eulalia
Fraigniaud, Pierre
Santoro, Nicola
Thilikos Touloupas, Dimitrios
This paper is concerned with the graph searching game. The search number es(G) of a graph G is the smallest number of searchers required to clear G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the connected version and of the monotone internal version of the graph searching problem comes from the fact that, as shown in the paper, none of these problems is minor closed for arbitrary graphs, as opposed to all known variants of the graph searching problem. Motivated by the fact that connected graph searching, and monotone internal graph searching are both minor closed in trees, we provide a complete characterization of the set of trees that can be cleared by a given number of searchers. In fact, we show that, in trees, there is only one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. This allows us to prove that, for any tree T, mis(T)= cs(T). For arbitrary graphs, we prove that there is a unique chain of inequalities linking all the search numbers above. More precisely, for any graph G, es(G)= is(G)= ms(G)leq mis(G)leq cs(G)= ics(G)leq mcs(G)=mics(G). The first two inequalities can be strict. In the case of trees, we have mics(G)leq 2 es(T)2, that is there are exactly 2 different search numbers in trees, and these search numbers differ by a factor of 2 at most.

Confección y gestión automática de exámenes tipo test
http://hdl.handle.net/2117/97260
Confección y gestión automática de exámenes tipo test
Cañadas Lorenzo, Juan Carlos; Diego Vives, José Antonio; Pelayo Melero, Ignacio Manuel
El presente trabajo describe la implementación de una aplicación informática como recurso docente, diseñada como plataforma para la elaboración, utilización y corrección de controles formativos y exámenes de evaluación. La principal finalidad de esta aplicación es poder facilitar la elaboración de diversos exámenes tipo test, tanto presenciales como no presenciales, con su correspondiente proceso de autocorrección, siendo así un software específico de evaluación a través de Internet. El programa que presentamos es ideal para llevar a cabo evaluaciones con
una gran variedad de preguntas empleadas de forma individual y simultánea para todos los estudiantes. Entre las ventajas de la aplicación, destacan, por un lado, su facilidad para generar una gran multiplicidad de exámenes independientes tanto para pruebas presenciales como para las no presenciales en donde el alumno puede hacer el examen de forma offline (imprimiendo un archivo pdf), y por otro, la posibilidad de enviar las respuestas dentro de un
tiempo predeterminado, mediante conexión a la red. Se trata de un software diseñado en el seno del Departamento de Física de la Universitat Politècnica de Catalunya (BarcelonaTech), y utilizado con gran éxito en sucesivas versiones, en las asignaturas de Física de las titulaciones de la ESEIAAT, la escuela de Ingeniería Industrial y Aeronáutica de Terrassa.
20161125T13:35:58Z
Cañadas Lorenzo, Juan Carlos
Diego Vives, José Antonio
Pelayo Melero, Ignacio Manuel
El presente trabajo describe la implementación de una aplicación informática como recurso docente, diseñada como plataforma para la elaboración, utilización y corrección de controles formativos y exámenes de evaluación. La principal finalidad de esta aplicación es poder facilitar la elaboración de diversos exámenes tipo test, tanto presenciales como no presenciales, con su correspondiente proceso de autocorrección, siendo así un software específico de evaluación a través de Internet. El programa que presentamos es ideal para llevar a cabo evaluaciones con
una gran variedad de preguntas empleadas de forma individual y simultánea para todos los estudiantes. Entre las ventajas de la aplicación, destacan, por un lado, su facilidad para generar una gran multiplicidad de exámenes independientes tanto para pruebas presenciales como para las no presenciales en donde el alumno puede hacer el examen de forma offline (imprimiendo un archivo pdf), y por otro, la posibilidad de enviar las respuestas dentro de un
tiempo predeterminado, mediante conexión a la red. Se trata de un software diseñado en el seno del Departamento de Física de la Universitat Politècnica de Catalunya (BarcelonaTech), y utilizado con gran éxito en sucesivas versiones, en las asignaturas de Física de las titulaciones de la ESEIAAT, la escuela de Ingeniería Industrial y Aeronáutica de Terrassa.

General bounds on limited broadcast domination
http://hdl.handle.net/2117/96711
General bounds on limited broadcast domination
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, Maria Luz; Cáceres, José
Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded by a constant k . The minimum cost of such a dominating broadcast is the k broadcast dominating number. We present a uni ed upper bound on this parameter for any value of k in terms of both k and the order of the graph. For the speci c case of the 2broadcast dominating number, we show that this bound is tight for graphs as large as desired. We also study the family of caterpillars, providing a smaller upper bound, which is attained by a set of such graphs with unbounded order.
20161116T10:37:47Z
Hernando Martín, María del Carmen
Mora Giné, Mercè
Pelayo Melero, Ignacio Manuel
Puertas, Maria Luz
Cáceres, José
Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded by a constant k . The minimum cost of such a dominating broadcast is the k broadcast dominating number. We present a uni ed upper bound on this parameter for any value of k in terms of both k and the order of the graph. For the speci c case of the 2broadcast dominating number, we show that this bound is tight for graphs as large as desired. We also study the family of caterpillars, providing a smaller upper bound, which is attained by a set of such graphs with unbounded order.