Graphs of order two less than the Moore bound

Title: Graphs of order two less than the Moore bound
Creator: Miller, Mirka; Simanjuntak, Rinovia
Date: 2008
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/39135
Identifier: vital:603
Identifier: https://doi.org/10.1016/j.disc.2006.06.045
Identifier: ISSN:0012-365X
Abstract: The Moore bound for a directed graph of maximum out-degree d and diameter k is Md,k=1+d+d2++dk. It is known that digraphs of order Md,k (Moore digraphs) do not exist for d>1 and k>1. Similarly, the Moore bound for an undirected graph of maximum degree d and diameter k is . Undirected Moore graphs only exist in a small number of cases. Mixed (or partially directed) Moore graphs generalize both undirected and directed Moore graphs. In this paper, we shall show that all known mixed Moore graphs of diameter k=2 are unique and that mixed Moore graphs of diameter k3 do not exist.; C1
Publisher: Elsevier
Relation: Discrete Mathematics Vol. 308, no. 13 (2008), p. 2810-2821
Rights: Copyright Elsevier
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Moore bound; Undirected graphs; Numerical methods; Problem solving; Degree diameter problems; Graph theory
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