COMBGRAF  Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
Wed, 02 Dec 2015 05:28:17 GMT
20151202T05:28:17Z

The automorphism group of a freebycyclic group in rank 2
http://hdl.handle.net/2117/79983
The automorphism group of a freebycyclic group in rank 2
Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric
Let
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)
Thu, 26 Nov 2015 17:54:44 GMT
http://hdl.handle.net/2117/79983
20151126T17:54:44Z
Bogopolski, Oleg
Martino, Armando
Ventura Capell, Enric
Let
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)

Locatingdominating sets and identifying codes in Graphs of Girth at least 5
http://hdl.handle.net/2117/78501
Locatingdominating sets and identifying codes in Graphs of Girth at least 5
Balbuena Martínez, Maria Camino Teófila; Foucaud, Florent; Hansberg Pastor, Adriana
Locatingdominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locatingdominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertexdisjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meeting these bounds.
Thu, 29 Oct 2015 13:30:57 GMT
http://hdl.handle.net/2117/78501
20151029T13:30:57Z
Balbuena Martínez, Maria Camino Teófila
Foucaud, Florent
Hansberg Pastor, Adriana
Locatingdominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locatingdominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertexdisjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meeting these bounds.

Completion and decomposition of a clutter into representable matroids
http://hdl.handle.net/2117/78129
Completion and decomposition of a clutter into representable matroids
Martí Farré, Jaume; Mier Vinué, Anna de
This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusionminimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.
Thu, 22 Oct 2015 11:23:00 GMT
http://hdl.handle.net/2117/78129
20151022T11:23:00Z
Martí Farré, Jaume
Mier Vinué, Anna de
This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusionminimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.

Perfect anda quasiperfect domination in trees
http://hdl.handle.net/2117/77007
Perfect anda quasiperfect domination in trees
Cáceres, Jose; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Tue, 22 Sep 2015 10:11:25 GMT
http://hdl.handle.net/2117/77007
20150922T10:11:25Z
Cáceres, Jose
Hernando Martín, María del Carmen
Mora Giné, Mercè
Pelayo Melero, Ignacio Manuel
Puertas, M. Luz

cCritical graphs with maximum degree three
http://hdl.handle.net/2117/76780
cCritical graphs with maximum degree three
Fiol Mora, Miquel Àngel
Let $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3edgecoloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3
edgecoloring of G can have is called the edgecoloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edgecoloring degree and, in particula.r, when
G is ccritical, that is $d(G) = c \ge 1$ and $d(G  e) < c$ for any
edge $e$ of $G$.
Tue, 15 Sep 2015 08:25:28 GMT
http://hdl.handle.net/2117/76780
20150915T08:25:28Z
Fiol Mora, Miquel Àngel
Let $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3edgecoloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3
edgecoloring of G can have is called the edgecoloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edgecoloring degree and, in particula.r, when
G is ccritical, that is $d(G) = c \ge 1$ and $d(G  e) < c$ for any
edge $e$ of $G$.

Distanceregular graphs where the distanced graph has fewer distinct eigenvalues
http://hdl.handle.net/2117/28555
Distanceregular graphs where the distanced graph has fewer distinct eigenvalues
Fiol Mora, Miquel Àngel; Brouwer, Andries
Let the Kneser graph K of a distanceregular graph $\Gamma$ be the graph on
the same vertex set as $\Gamma$, where two vertices are adjacent when they have
maximal distance in $\Gamma$. We study the situation where the BoseMesner
algebra of $\Gamma$ is not generated by the adjacency matrix of K. In particular,
we obtain strong results in the socalled `half antipodal' case.
Fri, 10 Jul 2015 09:38:58 GMT
http://hdl.handle.net/2117/28555
20150710T09:38:58Z
Fiol Mora, Miquel Àngel
Brouwer, Andries
Let the Kneser graph K of a distanceregular graph $\Gamma$ be the graph on
the same vertex set as $\Gamma$, where two vertices are adjacent when they have
maximal distance in $\Gamma$. We study the situation where the BoseMesner
algebra of $\Gamma$ is not generated by the adjacency matrix of K. In particular,
we obtain strong results in the socalled `half antipodal' case.

Almost every tree with m edges decomposes K2m,2m
http://hdl.handle.net/2117/28488
Almost every tree with m edges decomposes K2m,2m
Drmota, Michael; Lladó Sánchez, Ana M.
We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size. © Cambridge University Press 2013.
Wed, 01 Jul 2015 11:06:35 GMT
http://hdl.handle.net/2117/28488
20150701T11:06:35Z
Drmota, Michael
Lladó Sánchez, Ana M.
We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size. © Cambridge University Press 2013.

Classification of numerical 3semigroups by means of Lshapes
http://hdl.handle.net/2117/28487
Classification of numerical 3semigroups by means of Lshapes
Aguiló Gost, Francisco de Asis L.; Marijuan López, Carlos
We recall Lshapes, which are minimal distance diagrams, related to weighted 2Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate Lshapes to each numerical 3semigroup and we describe some main invariants of numerical 3semigroups in terms of their associated Lshapes. Finally, we give a characterization of the parameters of the Lshapes associated with a numerical 3semigroup in terms of its generators, and we use it to classify the numerical 3semigroups of interest in curve singularity.
Wed, 01 Jul 2015 11:02:05 GMT
http://hdl.handle.net/2117/28487
20150701T11:02:05Z
Aguiló Gost, Francisco de Asis L.
Marijuan López, Carlos
We recall Lshapes, which are minimal distance diagrams, related to weighted 2Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate Lshapes to each numerical 3semigroup and we describe some main invariants of numerical 3semigroups in terms of their associated Lshapes. Finally, we give a characterization of the parameters of the Lshapes associated with a numerical 3semigroup in terms of its generators, and we use it to classify the numerical 3semigroups of interest in curve singularity.

On global locationdomination in bipartite graphs
http://hdl.handle.net/2117/28318
On global locationdomination in bipartite graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Tue, 16 Jun 2015 09:42:50 GMT
http://hdl.handle.net/2117/28318
20150616T09:42:50Z
Hernando Martín, María del Carmen
Mora Giné, Mercè
Pelayo Melero, Ignacio Manuel

On global locationdomination in graphs
http://hdl.handle.net/2117/28254
On global locationdomination in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A dominating set S of a graph G is called locatingdominating, LDset for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LDcodes and the cardinality of an LDcode is the locationdomination number lambda(G). An LDset S of a graph G is global if it is an LDset of both G and its complement G'. The global locationdomination number lambda g(G) is introduced as the minimum cardinality of a global LDset of G.
In this paper, some general relations between LDcodes and the locationdomination number in a graph and its complement are presented first.
Next, a number of basic properties involving the global locationdomination number are showed. Finally, both parameters are studied indepth for the family of blockcactus graphs.
Wed, 10 Jun 2015 11:51:21 GMT
http://hdl.handle.net/2117/28254
20150610T11:51:21Z
Hernando Martín, María del Carmen
Mora Giné, Mercè
Pelayo Melero, Ignacio Manuel
A dominating set S of a graph G is called locatingdominating, LDset for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LDcodes and the cardinality of an LDcode is the locationdomination number lambda(G). An LDset S of a graph G is global if it is an LDset of both G and its complement G'. The global locationdomination number lambda g(G) is introduced as the minimum cardinality of a global LDset of G.
In this paper, some general relations between LDcodes and the locationdomination number in a graph and its complement are presented first.
Next, a number of basic properties involving the global locationdomination number are showed. Finally, both parameters are studied indepth for the family of blockcactus graphs.