✦ LIBER ✦

Connectivity of cages

✍ Scribed by Fu, H. L.; Huang, K. C.; Rodger, C. A.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 85 KB
Volume: 24
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199702)24:2<187::aid-jgt6>3.0.co;2-m

No coin nor oath required. For personal study only.

✦ Synopsis

A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such there exists a (k; g)-graph with ν 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; g 1 ) < f(k; g 2 ) for all k ≥ 3 and 3 ≤ g 1 < g 2 . We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k.

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