COMBGRAF  Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
20150904T02:10:20Z

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.
20150101T00:00:00Z

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.
20140101T00:00:00Z

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.
20140601T00:00:00Z

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
20150610T00:00:00Z

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.
20150529T00:00:00Z

Oxidative stress is a central target for physical exercise neuroprotection against pathological brain aging
http://hdl.handle.net/2117/27948
Oxidative stress is a central target for physical exercise neuroprotection against pathological brain aging
GarciaMesa, Yoelvis; Colie, Sandra; Corpas, Ruben; Cristofol, Rosa; Comellas Padró, Francesc de Paula; Nebreda, Angel; GiménezLlort, Lydia; Sanfeliu, Coral
Physical exercise is suggested for preventing or delaying senescence and Alzheimer’s disease (AD). We have examined its therapeutic value in the advanced stage of ADlike pathology in 3xTgAD female mice through voluntary wheel running from 12 to 15 months of age. Mice submitted to exercise showed improved body fitness, immunorejuvenation, improvement of behavior and cognition, and reduced amyloid and tau pathology. Brain tissue analysis of aged 3xTgAD mice showed high levels of oxidative damage. However, this damage was decreased by physical exercise through regulation of redox homeostasis. Network analyses showed that oxidative stress was a central event, which correlated with ADlike pathology and the ADrelated behaviors of anxiety, apathy, and cognitive loss. This study corroborates the importance of redox mechanisms in the neuroprotective effect of physical exercise, and supports the theory of the crucial role of oxidative stress in the switch from normal brain aging to pathological aging and AD.
20150226T00:00:00Z

Decomposing almost complete graphs by random trees
http://hdl.handle.net/2117/27908
Decomposing almost complete graphs by random trees
Lladó Sánchez, Ana M.
An old conjecture of Ringel states that every tree with m edges decom poses the complete graph K 2 m +1 . A more general version of the Ringel’s conjecture says that every tree with m edges decomposes K rm +1 for each r = 2 provided that r and m + 1 are not both odd. The best lower bound for the order of a complete graph decomposed by a given tree with m edge is O ( m 3 ). We show that asymptotically almost surely a random tree with m edges and p = 2 m + 1 is a prime decomposes the complete graph minus one edge K 3 p  e . We also show that, for every prime of the form 2 km + 1 a random tree with m edges asymptotically almost surely decomposes the graph K 2 km +1 (3) obtained from the complete graph by replacing each vertex by the complement of a triangle.
20140101T00:00:00Z

A new application of the $\otimes_h$product to $\alpha$labelings
http://hdl.handle.net/2117/27897
A new application of the $\otimes_h$product to $\alpha$labelings
López Masip, Susana Clara; Muntaner Batle, Francesc Antoni
The weak tensor product was introduced by Snevily as a way to construct new graphs that admit alabelings from a pair of known agraphs. In this article, we show that this product and the application to alabelings can be generalized by considering as a second factor of the product, a family G of bipartite (p, q)graphs, p and q fixed. The only additional restriction that we should consider is that for every F ¿ G , there exists an alabeling fF with fF (V(F )) = L¿H, where L, H ¿ [0, q] are the stable sets induced by the characteristic of fF and they do not depend on F .Wealso obtain analogous applications to near alabelings and bigraceful labelings.
20150101T00:00:00Z

Caracterizaciones combinatorias y algebraicas de grafos distanciaregulares
http://hdl.handle.net/2117/27894
Caracterizaciones combinatorias y algebraicas de grafos distanciaregulares
Fiol Mora, Miquel Àngel
Los grafos distanciaregulares aparecen a menudo en el estudio de es
tructuras matemáticas con un alto grado de simetría y/o regularidad. Un ejemplo bien conocido de tales grafos son los esqueletos de los sólidos platónicos. Desde que fueron propuestos por Norman Biggs, los grafos distanciaregulares han sido caracterizados por numerosos resultados, tanto de carácter combinatorio como algebraico. Como ejemplo del primer caso, sabemos que un grafo es distanciaregular si, y sólo si, el número de caminos de una longitud dada entre dos vértices sólo depende de la distancia entre dichos vértices. En esta charla se van a presentar y comparar las diferentes caracterizaciones conocidas, tanto las más clásicas como las que han sido recientemente descubiertas por el conferenciante y algunos de sus colaboradores. Entre las últimas, cabe destacar el que ya es conocido en la literatura com el `teorema del exceso espectral’. Este resultado puede considerarse como una caracterización casiespectral, y afirma que un grafo es distanciaregular si, y sólo si, su exceso espectral (una cantidad calculable a partir de su matriz de adyacencia) es igual a su exceso medio (el número medio de vértices a distancia máxima de cada vértice).
20140101T00:00:00Z

An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs
http://hdl.handle.net/2117/27893
An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs
Abiad, Aida; Fiol Mora, Miquel Àngel; Haemers, Willem H.; Perarnau Llobet, Guillem
We apply eigenvalue interlacing techniques for obtaining lower and upper
bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality.
This leads to generalizations of, and variations on theorems by Grone, and Grone &
Merris. As a consequence we obtain inequalities involving bounds for some wellknown
parameters of a graph, such as edgeconnectivity, and the isoperimetric number.
20140101T00:00:00Z