COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
Fri, 20 Jan 2017 05:52:22 GMT2017-01-20T05:52:22ZAbelian 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 non-constructive.
Tue, 17 Jan 2017 08:34:07 GMThttp://hdl.handle.net/2117/993922017-01-17T08:34:07ZAguiló Gost, Francisco de Asis L.Fiol Mora, Miquel ÀngelPérez Mansilla, SoniaAbelian 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 non-constructive.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 distance-related parameters (mainly, the diameter and the average distance) of sequence mixed graphs are presented.
Wed, 21 Dec 2016 08:37:00 GMThttp://hdl.handle.net/2117/986762016-12-21T08:37:00ZDalfó Simó, CristinaFiol Mora, Miquel ÀngelLópez, NachoA 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 distance-related 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.
Tue, 29 Nov 2016 13:30:39 GMThttp://hdl.handle.net/2117/974222016-11-29T13:30:39ZBarrière Figueroa, EulaliaFraigniaud, PierreSantoro, NicolaThilikos Touloupas, DimitriosThis 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.
Fri, 25 Nov 2016 13:35:58 GMThttp://hdl.handle.net/2117/972602016-11-25T13:35:58ZCañadas Lorenzo, Juan CarlosDiego Vives, José AntonioPelayo Melero, Ignacio ManuelEl 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 2-broadcast 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.
Wed, 16 Nov 2016 10:37:47 GMThttp://hdl.handle.net/2117/967112016-11-16T10:37:47ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelPuertas, Maria LuzCáceres, JoséLimited 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 2-broadcast 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.Algorithmic recognition of infinite cyclic extensions
http://hdl.handle.net/2117/96690
Algorithmic recognition of infinite cyclic extensions
Cavallo, Bren; Delgado Rodríguez, Jordi; Kahrobaei, Delaram; Ventura Capell, Enric
We prove that one cannot algorithmically decide whether a finitely presented Z-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the equivalence between the isomorphism problem within the subclass of unique Z-extensions, and the semi-conjugacy problem for deranged outer automorphisms.
Tue, 15 Nov 2016 16:32:01 GMThttp://hdl.handle.net/2117/966902016-11-15T16:32:01ZCavallo, BrenDelgado Rodríguez, JordiKahrobaei, DelaramVentura Capell, EnricWe prove that one cannot algorithmically decide whether a finitely presented Z-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the equivalence between the isomorphism problem within the subclass of unique Z-extensions, and the semi-conjugacy problem for deranged outer automorphisms.Symmetry breaking in tournaments
http://hdl.handle.net/2117/91158
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 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.
Thu, 27 Oct 2016 11:29:19 GMThttp://hdl.handle.net/2117/911582016-10-27T11:29:19ZLozano Bojados, AntoniWe provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices S 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.Distance mean-regular graphs
http://hdl.handle.net/2117/91052
Distance mean-regular graphs
Fiol Mora, Miquel Àngel; Diego, Victor
We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V , the averages of the intersection numbers p h ij (u, v) = |Gi(u) n Gj (v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance h ¿ {0, 1, . . . , D} from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of G and, hence, they generate a subalgebra of A. Some other algebras associated to distance mean-regular graphs are also characterized.
Tue, 25 Oct 2016 09:46:43 GMThttp://hdl.handle.net/2117/910522016-10-25T09:46:43ZFiol Mora, Miquel ÀngelDiego, VictorWe introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V , the averages of the intersection numbers p h ij (u, v) = |Gi(u) n Gj (v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance h ¿ {0, 1, . . . , D} from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of G and, hence, they generate a subalgebra of A. Some other algebras associated to distance mean-regular graphs are also characterized.José Gómez Martí 1968-2014: in memoriam
http://hdl.handle.net/2117/89974
José Gómez Martí 1968-2014: in memoriam
Fiol Mora, Miquel Àngel
Fri, 16 Sep 2016 10:33:15 GMThttp://hdl.handle.net/2117/899742016-09-16T10:33:15ZFiol Mora, Miquel ÀngelA note on the order of iterated line digraphs
http://hdl.handle.net/2117/89923
A note on the order of iterated line digraphs
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal
polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.
Wed, 14 Sep 2016 12:40:26 GMThttp://hdl.handle.net/2117/899232016-09-14T12:40:26ZDalfó Simó, CristinaFiol Mora, Miquel ÀngelGiven a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal
polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.