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We consider the bipartite version of the degree/diameter problem, namely, given natural numbers ∆ ≥ 2 and D ≥ 2, find the maximum number N b (∆, D) of vertices in a bipartite graph of maximum degree ∆ and diameter D. In this context, the Moore bipartite bound M b (∆, D) represents an upper bound for N b (∆, D). Bipartite graphs of maximum degree ∆, diameter… (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… (More)

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 em-beddable 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… (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)

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