Guillermo Pineda-Villavicencio

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It is known that the Moore bipartite bound provides an upper bound on the order of a connected bipartite graph. In this paper we deal with bipartite graphs of maximum degree ∆ ≥ 2, diameter D ≥ 2 and defect 2 (having 2 vertices less than the Moore bipartite bound). We call such graphs bipartite (∆, D, −2)-graphs. We find that the eigenvalues other than ±∆(More)
The Moore bound constitutes both an upper bound on the order of a graph of maximum degree d and diameter D = k and a lower bound on the order of a graph of minimum degree d and odd girth g = 2k + 1. Graphs missing or exceeding the Moore bound by ǫ are called graphs with defect or excess ǫ, respectively. While Moore graphs (graphs with ǫ = 0) and graphs with(More)
We consider bipartite graphs of degree ∆ ≥ 2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (∆, 3, −2)-graphs.graph. We also prove several necessary conditions for the existence of bipartite (∆, 3, −2)-graphs. The most general of these conditions is that either ∆ or ∆ − 2 must be a(More)
The Moore bipartite bound represents an upper bound on the order of a bipartite graph of maximum degree ∆ and diameter D. Bipartite graphs of maximum degree ∆, diameter D and order equal to the Moore bipartite bound are called Moore bipartite graphs. Such bipartite graphs exist only if D = 2, 3, 4 and 6, and for D = 3, 4, 6, they have been constructed only(More)
We introduce the problem of finding the largest subgraph of a given weighted undirected graph (host graph), subject to constraints on the maximum degree and the diameter. We discuss some applications in security, network design and parallel processing, and in connection with the latter we derive some bounds for the order of the largest subgraph in host(More)
In the pursuit of obtaining largest graphs of given maximum degree ∆ and diameter D, many construction techniques have been developed. Compounding of graphs is one such technique. In this paper, by means of the compounding of complete graphs into a Moore bipartite graph of diameter 6, we obtain a family of large graphs of the same diameter. 1 maximum(More)
Given a tesselation of the plane, defined by a planar straight-line graph G, we want to find a minimal set S of points in the plane, such that the Voronoi diagram associated with S 'fits' G. This is the Generalized Inverse Voronoi Problem (GIVP), defined in [12] and rediscovered recently in [3]. Here we give an algorithm that solves this problem with a(More)
Large scale networks have become ubiquitous elements of our society. Modern social networks , supported by communication and travel technology, have grown in size and complexity to unprecedented scales. Computer networks, such as the Internet, have a fundamental impact on commerce, politics and culture. The study of networks is also central in biology,(More)