On bipartite graphs of diameter 3 and defect 2

Title: On bipartite graphs of diameter 3 and defect 2
Creator: Delorme, Charles; Jorgensen, Leif; Miller, Mirka; Pineda-Villavicencio, Guillermo
Date: 2009
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/41411
Identifier: vital:1921
Identifier: https://doi.org/10.1002/jgt.20378
Identifier: ISSN:0364-9024
Abstract: We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (â–³,3, -2) -graphs. We prove the uniqueness of the known bipartite (3, 3, -2) -graph and bipartite (4, 3, -2)-graph. We also prove several necessary conditions for the existence of bipartite (â–³,3, -2) - graphs. The most general of these conditions is that either â–³ or â–³-2 must be a perfect square. Furthermore, in some cases for which the condition holds, in particular, when â–³ = 6 and â–³ = 9, we prove the non-existence of the corresponding bipartite (â–³,3,-2)-graphs, thus establishing that there are no bipartite (â–³,3, -2)-graphs, for 5
Relation: Journal of Graph Theory Vol. 61, no. 4 (2009), p. 271-288
Rights: Copyright John Wiley & Sons
Rights: Open Access
Rights: This metadata is freely available under a CCO license
Subject: Bipartite Moore bound; Bipartite Moore graphs; Defect; Degree diameter problem for bipartite graphs
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