COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
The research of COMBGRAPH deals with extremal problems in Combinatorics and Graph Theory. The study of discrete configurations (which optimize one or several parameters) is a main source of challenges. This project includes problems related to: the optimization of metric parameters of graphs, coloring and labeling problems, connectivity and reliability, configurations in graphs, symmetric structures, tilings, algorithm design, and signal processing techniques. All these problems are mainly motivated by applications in network design, analysis for communication protocols, multiprocessor systems, and complex networks. We use combinatorial and algebraic techniques in graph theory, Fourier analysis and polynomial and probabilistic methods in combinatorics, together with techniques close to the combinatorial nature of the problems under consideration. This project gathers the activity of a well-established research group with almost 30 years of experience and with international projection.
Collections in this community
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Altres [1]
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Articles de revista [290]
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Capítols de llibre [22]
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Reports de recerca [40]
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Working papers [1]
Recent Submissions
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Contiguous and internal graph searching
(2002)
Research report
Open AccessIn the graph searching problem, we are given a graph whose edges are all "contaminated", and, via a sequence of "steps" using "searchers", we want to obtain a state of the graph in which all edges are simultaneously "clear". ... -
On the non-uniform complexity of the Graph Isomorphism problem
(1992-02-19)
Research report
Open AccessWe study the non-uniform complexity of the Graph Isomorphism (GI) and Graph Automorphism (GA) problems considering the implications of different types of polynomial time reducibilitites from these problems to sparse sets. ... -
Some product graphs with power dominating number at most 2
(Elsevier, 2021-07-08)
Article
Open AccessLet S be a set of vertices of a graph G. Let M[S] be the set of vertices built from the closed neighborhood N[S] of S, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its ... -
On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
(Taylor & Francis, 2022-02-19)
Article
Open AccessThe universal adjacency matrix U of a graph G, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, ... -
Optimization of eigenvalue bounds for the independence and chromatic number of graph powers
(2022-03)
Article
Open AccessThe k-thpower of a graph G=(V,E), G^k, is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for ... -
Some results on the laplacian spectra of Token graphs
(Springer, 2021)
Conference report
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ... -
On symmetric association schemes and associated quotient-polynomial graphs
(2021-01-01)
Article
Open AccessLet denote an undirected, connected, regular graph with vertex set , adjacency matrix , and distinct eigenvalues. Let denote the subalgebra of generated by . We refer to as the adjacency algebra of . In this paper we ... -
On the Laplacian spectra of token graphs
(Elsevier, 2021-09-15)
Article
Open AccessWe study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever ... -
New cyclic Kautz digraphs with optimal diameter
(2021)
Article
Open AccessWe obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree, there is no other digraph with a smaller diameter. This new family of digraphs are called `modified cyclic ... -
Spectra and eigenspaces of arbitrary lifts of graphs
(2021-09)
Article
Open AccessWe describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not). -
Trees whose even-degree vertices induce a path are antimagic
(2022-08)
Article
Open AccessAn antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels ... -
Uniform forcing and immune sets in graphs and hypergraphs
(2021-12-31)
Article
Open AccessZero forcing is an iterative coloring process on a graph that has been widely used in such different areas as the modelling of propagation phenomena in networks and the study of minimum rank problems in matrices and graphs. ...
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