Non-existence of bipartite graphs of diameter at least \(4\) and defect \(2\)
type: Item
instance of: scholarly article
title: Non-existence of bipartite graphs of diameter at least \(4\) and defect \(2\)
zbMATH Open document ID: 1238.05076
author: Guillermo Pineda-Villavicencio
published in: Journal of Algebraic Combinatorics
publication date: 2011-11-07T00:00:00Z
review text: This paper proves a conjecture by settling the non-existence of bipartite \((\Delta,D,-2)\) graphs for all \(\Delta \geq 3\) and all \(D \geq 6\), using the reasoning in the proofs of the non-existence of Moore graphs for \(\Delta\geq 3\) and \(D\geq 3\) and the non-existence of regular graphs of degree \(\Delta\geq 3\), even girth \(g\geq 2\) and order \(M^b_{\Delta,g/2}+2\) and the non-existence of regular graphs of \(\Delta\geq 3\) odd girth \(g\geq 5\) and order \(M_{\Delta,(g-1)/2}+1\).
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 5968633
zbMATH Keywords: degree/diameter problem
zbMATH Keywords: Moore bipartite bound
zbMATH Keywords: Moore bipartite graphs, Dickson polynomials of the second kind
zbMATH Keywords: Moore graphs
reviewed by: G. N. Prasanth
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: s10801-010-0266-0
OpenAlex ID: W2001852268
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DOI: 10.1007/S10801-010-0266-0
description: scientific article; zbMATH DE number 5968633