The minimum number of vertices with girth 6 and degree set D = {r,m}

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Detail(s)

Original languageEnglish
Pages (from-to)249-258
Journal / PublicationDiscrete Mathematics
Volume269
Issue number1-3
Publication statusPublished - 28 Jul 2003
Externally publishedYes

Abstract

A (D;g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D;g) the number of vertices in a (D;g)-cage. In this paper it is shown that f({r,m};6)≥2(rm-m+1) for any 2≤r<m, and f({r,m};6)=2(rm-m+1) if either (i) 2≤r≤5 and r<m or (ii) m-1 is a prime power and 2≤r<m. Upon these results, it is conjectured that f({r,m};6)=2(rm-m+1) for any r with 2≤r<m. © 2002 Elsevier B.V. All rights reserved.

Research Area(s)

  • Cage, Degree set, Girth, Symmetric graph

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