Connectivity of Cages

Hung-Lin Fu*, K. C. Huang, C. A. Rodger

*Corresponding author for this work

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

A (k; g)-graph is a k-regular graph with girth g. Let f(k; g) be the smallest integer v such there exists a (k; g)-graph with v vertices. A (k; g)-cage is a (k; g)-graph with f(k; g) vertices. In this paper we prove that the cages are monotonic in that f(k; g1) < f(k; g2) for all k ≥ 3 and 3 ≤ g1 ≤ g2. We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k.

Original languageEnglish
Pages (from-to)187-191
Number of pages5
JournalJournal of Graph Theory
Volume24
Issue number2
DOIs
StatePublished - 1 Jan 1997

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