- 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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