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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 ... -
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. ... -
Bipartite biregular Moore graphs
(2021-11)
Article
Open AccessA bipartite graph G = (V, E) with V = V1 ¿ V2 is biregular if all the vertices of a stable set Vi have the same degree ri for i = 1, 2. In this paper, we give an improved new Moore bound for an infinite family of such ... -
On d-Fibonacci digraphs
(2021-10-03)
Article
Open AccessThe d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we ... -
Decompositions of a rectangle into non-congruent rectangles of equal area
(2021-06)
Article
Open AccessIn this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called ‘Mondrian art problem’ that asks a ...
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