Ramiro Feria-Purón

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We consider the degree/diameter problem for graphs embedded in a surface, namely, given a surface Σ and integers ∆ and k, determine the maximum order N(∆, k,Σ) of a graph embeddable in Σ with maximum degree ∆ and diameter k. We introduce a number of constructions which produce many new largest known planar and toroidal graphs. We record all these graphs in(More)
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with particular classes of graphs and methods. Here we approach the problem from the computational viewpoint, and in a quite general(More)
In this paper we consider the degree/diameter problem, namely, given natural numbers ∆ ≥ 2 and D ≥ 1, find the maximum number N(∆,D) of vertices in a graph of maximum degree ∆ and diameter D. In this context, the Moore bound M(∆,D) represents an upper bound for N(∆,D). Graphs of maximum degree ∆, diameter D and order M(∆,D), called Moore graphs, turned out(More)
<lb>In this talk, we introduce two kinds of power for graphs [2, 3]. First,<lb>for a given graph G, we consider G<lb>r<lb>s<lb>, i.e., the rth power of the sth<lb>subdivision of G, and we present some basic properties of this power. In the sequel, we introduce the graph power G<lb>2s+1<lb>2̃r+1<lb>. We show that<lb>these powers can be considered as the dual(More)
We consider the bipartite version of the degree/diameter problem, namely, given natural numbers ∆ ≥ 2 and D ≥ 2, find the maximum number Nb(∆,D) of vertices in a bipartite graph of maximum degree ∆ and diameter D. In this context, the Moore bipartite bound Mb(∆,D) represents an upper bound for Nb(∆,D). Bipartite graphs of maximum degree ∆, diameter D and(More)
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