DSpace Collection:
http://hdl.handle.net/2117/3180
Tue, 30 Jun 2015 13:11:15 GMT2015-06-30T13:11:15Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoOn global location-domination in bipartite graphs
http://hdl.handle.net/2117/28318
Title: On global location-domination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelTue, 16 Jun 2015 09:42:50 GMThttp://hdl.handle.net/2117/283182015-06-16T09:42:50ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoDomination, Global domination, Locating domination, Complement graph, Bipartite graph.Approximate results for rainbow labelings
http://hdl.handle.net/2117/27843
Title: Approximate results for rainbow labelings
Authors: Lladó Sánchez, Ana M.
Description: Article de recercaFri, 08 May 2015 11:21:05 GMThttp://hdl.handle.net/2117/278432015-05-08T11:21:05ZLladó Sánchez, Ana M.noOn star-forest ascending subgraph decomposition
http://hdl.handle.net/2117/27841
Title: On star-forest ascending subgraph decomposition
Authors: Aroca Farrerons, José María; Lladó Sánchez, Ana M.Fri, 08 May 2015 11:15:42 GMThttp://hdl.handle.net/2117/278412015-05-08T11:15:42ZAroca Farrerons, José María; Lladó Sánchez, Ana M.noDecomposing almost complete graphs by random trees
http://hdl.handle.net/2117/27840
Title: Decomposing almost complete graphs by random trees
Authors: Lladó Sánchez, Ana M.Fri, 08 May 2015 11:13:27 GMThttp://hdl.handle.net/2117/278402015-05-08T11:13:27ZLladó Sánchez, Ana M.noOn perfect and quasiperfect domination in graphs
http://hdl.handle.net/2117/27709
Title: On perfect and quasiperfect domination in graphs
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M LuzMon, 04 May 2015 10:26:03 GMThttp://hdl.handle.net/2117/277092015-05-04T10:26:03ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M LuznoGlobal location-domination in graphs
http://hdl.handle.net/2117/27680
Title: Global location-domination in graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set S of a graph G is called
locating-dominating, LD-setfor short, if every vertex v not in S is uniquely determined by the set of neighbors of v
belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the
location-domination number (G). An LD-set
S of a graph G is global if it is an LD-set of both G and its complement G. The
global location-domination number g(G) is the minimum cardinality of a global LD-set of
G. In this work,we give some relations between locating-dominating sets and the location-domination number in a graph and its complement
Description: Domination, Global domination, Locating domination, Complement graph, Block-cactus, TreesThu, 30 Apr 2015 08:12:31 GMThttp://hdl.handle.net/2117/276802015-04-30T08:12:31ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoA dominating set S of a graph G is called
locating-dominating, LD-setfor short, if every vertex v not in S is uniquely determined by the set of neighbors of v
belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the
location-domination number (G). An LD-set
S of a graph G is global if it is an LD-set of both G and its complement G. The
global location-domination number g(G) is the minimum cardinality of a global LD-set of
G. In this work,we give some relations between locating-dominating sets and the location-domination number in a graph and its complementJacobi matrices and boundary value problems in distance-regular graphs
http://hdl.handle.net/2117/14821
Title: Jacobi matrices and boundary value problems in distance-regular graphs
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia
Abstract: 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.Thu, 26 Jan 2012 10:21:55 GMThttp://hdl.handle.net/2117/148212012-01-26T10:21:55ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, SilvianoIn 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.A differential approach for bounding the index of graphs under perturbations
http://hdl.handle.net/2117/12078
Title: A differential approach for bounding the index of graphs under perturbations
Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, ErnestFri, 25 Mar 2011 15:57:30 GMThttp://hdl.handle.net/2117/120782011-03-25T15:57:30ZDalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, ErnestnoGraph, Adjacency matrix, Spectral radius, Graph perturbation, Di erential inequalitiesEdge-distance-regular graphs
http://hdl.handle.net/2117/11794
Title: Edge-distance-regular graphs
Authors: Cámara Vallejo, Marc; Dalfó Simó, Cristina; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Abstract: 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.Mon, 14 Mar 2011 08:32:42 GMThttp://hdl.handle.net/2117/117942011-03-14T08:32:42ZCámara Vallejo, Marc; Dalfó Simó, Cristina; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, ErnestnoEdge-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.Connected graph searching
http://hdl.handle.net/2117/9116
Title: Connected graph searching
Authors: Barrière Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos Touloupas, Dimitrios
Abstract: In graph searching game the opponents are a set of searchers and a fugitive in a graph.
The searchers try to capture the fugitive by applying some sequence moves that include
placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture
by moving along unguarded paths. The search number of a graph is the minimum number
of searchers required to guarantee the capture of the fugitive. In this paper, we initiate
the study of this game under the natural restriction of connectivity where we demand that
in each step of the search the locations of the graph that are clean (i.e. non-accessible to
the fugitive) remain connected. We give evidence that many of the standard mathematical
tools used so far in the classic graph searching fail under the connectivity requirement. We
also settle the question on “the price of connectivity” that is how many searchers more
are required for searching a graph when the connectivity demand is imposed. We make
estimations of the price of connectivity on general graphs and we provide tight bounds
for the case of trees. In particular for an n-vertex graph the ratio between the connected
searching number and the non-connected one is O(log n) while for trees this ratio is always
at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for
all graphs. Our combinatorial results imply a complete characterization of connected graph
searching on trees. It is based on a forbidden-graph characterization of the connected search
number. We prove that the connected search game is monotone for trees, i.e. restricting
search strategies to only those where the clean territories increase monotonically does not
require more searchers. A consequence of our results is that the connected search number can
be computed in polynomial time on trees, moreover, we show how to make this algorithm
distributed. Finally, we reveal connections of this parameter to other invariants on trees
such as the Horton-Stralher number.Mon, 27 Sep 2010 17:25:19 GMThttp://hdl.handle.net/2117/91162010-09-27T17:25:19ZBarrière Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos Touloupas, DimitriosnoGraph searching, Cops-and-robbers, Network securityIn graph searching game the opponents are a set of searchers and a fugitive in a graph.
The searchers try to capture the fugitive by applying some sequence moves that include
placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture
by moving along unguarded paths. The search number of a graph is the minimum number
of searchers required to guarantee the capture of the fugitive. In this paper, we initiate
the study of this game under the natural restriction of connectivity where we demand that
in each step of the search the locations of the graph that are clean (i.e. non-accessible to
the fugitive) remain connected. We give evidence that many of the standard mathematical
tools used so far in the classic graph searching fail under the connectivity requirement. We
also settle the question on “the price of connectivity” that is how many searchers more
are required for searching a graph when the connectivity demand is imposed. We make
estimations of the price of connectivity on general graphs and we provide tight bounds
for the case of trees. In particular for an n-vertex graph the ratio between the connected
searching number and the non-connected one is O(log n) while for trees this ratio is always
at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for
all graphs. Our combinatorial results imply a complete characterization of connected graph
searching on trees. It is based on a forbidden-graph characterization of the connected search
number. We prove that the connected search game is monotone for trees, i.e. restricting
search strategies to only those where the clean territories increase monotonically does not
require more searchers. A consequence of our results is that the connected search number can
be computed in polynomial time on trees, moreover, we show how to make this algorithm
distributed. Finally, we reveal connections of this parameter to other invariants on trees
such as the Horton-Stralher number.Strong product of graphs: Geodetic and hull number and boundary-type sets
http://hdl.handle.net/2117/8413
Title: Strong product of graphs: Geodetic and hull number and boundary-type sets
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María LuzTue, 27 Jul 2010 09:58:31 GMThttp://hdl.handle.net/2117/84132010-07-27T09:58:31ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María LuznoStrong product, geodetic number, bull number, boundary-type setsMean first-passage time for random walks on generalized deterministic recursive trees
http://hdl.handle.net/2117/7385
Title: Mean first-passage time for random walks on generalized deterministic recursive trees
Authors: Comellas Padró, Francesc de Paula; Miralles de la Asunción, AliciaWed, 26 May 2010 15:13:42 GMThttp://hdl.handle.net/2117/73852010-05-26T15:13:42ZComellas Padró, Francesc de Paula; Miralles de la Asunción, AlicianoGraphs, Friends and Acquaintances
http://hdl.handle.net/2117/7159
Title: Graphs, Friends and Acquaintances
Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Abstract: As is well known, a graph is a mathematical object modeling the
existence of a certain relation between pairs of elements of a given set.
Therefore, it is not surprising that many of the first results concerning
graphs made reference to relationships between people or groups of
people. In this article, we comment on four results of this kind, which
are related to various general theories on graphs and their applications:
the Handshake lemma (related to graph colorings and Boolean
algebra), a lemma on known and unknown people at a cocktail party
(to Ramsey theory), a theorem on friends in common (to distanceregularity
and coding theory), and Hall’s Marriage theorem (to the
theory of networks). These four areas of graph theory, often with
problems which are easy to state but difficult to solve, are extensively
developed and currently give rise to much research work. As examples
of representative problems and results of these areas, which are
discussed in this paper, we may cite the following: the Four Colors
Theorem (4CTC), the Ramsey numbers, problems of the existence of
distance-regular graphs and completely regular codes, and finally the
study of topological proprieties of interconnection networks.Tue, 11 May 2010 15:41:55 GMThttp://hdl.handle.net/2117/71592010-05-11T15:41:55ZDalfó Simó, Cristina; Fiol Mora, Miquel ÀngelnoGraph, Edge-coloring, Boolean Algebra, Ramsey Theory, Distance-regularity, Spectral Graph Theory, Completely Regular Code, Hall¿s
Marriage Theorem, Menger¿s TheoremAs is well known, a graph is a mathematical object modeling the
existence of a certain relation between pairs of elements of a given set.
Therefore, it is not surprising that many of the first results concerning
graphs made reference to relationships between people or groups of
people. In this article, we comment on four results of this kind, which
are related to various general theories on graphs and their applications:
the Handshake lemma (related to graph colorings and Boolean
algebra), a lemma on known and unknown people at a cocktail party
(to Ramsey theory), a theorem on friends in common (to distanceregularity
and coding theory), and Hall’s Marriage theorem (to the
theory of networks). These four areas of graph theory, often with
problems which are easy to state but difficult to solve, are extensively
developed and currently give rise to much research work. As examples
of representative problems and results of these areas, which are
discussed in this paper, we may cite the following: the Four Colors
Theorem (4CTC), the Ramsey numbers, problems of the existence of
distance-regular graphs and completely regular codes, and finally the
study of topological proprieties of interconnection networks.Bounds on the size of super edge-magic graphs depending on the girth
http://hdl.handle.net/2117/7063
Title: Bounds on the size of super edge-magic graphs depending on the girth
Authors: Ichishima, Rikio; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
Abstract: Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic
graph then q 2p−3. Furthermore, if G is super edge-magic and q = 2p−3, then the girth
of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then
q 2p − 5. In this paper we show that there are infinitely many graphs which are super
edge-magic, have girth 5, and q = 2p−5. Therefore the maximum size for super edge-magic
graphs of girth 5 cannot be reduced with respect to the maximum size of super edge-magic
graphs of girth 4.Thu, 22 Apr 2010 17:19:00 GMThttp://hdl.handle.net/2117/70632010-04-22T17:19:00ZIchishima, Rikio; Muntaner Batle, Francesc Antoni; Rius Font, MiquelnoLet G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic
graph then q 2p−3. Furthermore, if G is super edge-magic and q = 2p−3, then the girth
of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then
q 2p − 5. In this paper we show that there are infinitely many graphs which are super
edge-magic, have girth 5, and q = 2p−5. Therefore the maximum size for super edge-magic
graphs of girth 5 cannot be reduced with respect to the maximum size of super edge-magic
graphs of girth 4.On Almost Distance-Regular Graphs
http://hdl.handle.net/2117/6749
Title: On Almost Distance-Regular Graphs
Authors: Dalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, BramMon, 22 Mar 2010 13:02:28 GMThttp://hdl.handle.net/2117/67492010-03-22T13:02:28ZDalfó Simó, Cristina; Van Dam, Edwin; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gorissen, Bramno