Super cyclically edge connected transitive graphs

Authors:
Zhao Zhang;Bing Wang
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, P.R. China 830046;College of Mathematics and System Sciences, Xinjiang University, Urumqi, P.R. China 830046
Venue:
Journal of Combinatorial Optimization
Year:
2011

Citing 4
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Abstract

A cyclic edge-cut of a graph G is an edge set, the removal of which separates two cycles. If G has a cyclic edge-cut, then it is called cyclically separable. For a cyclically separable graph G, the cyclic edge-connectivity 驴 c (G) is the cardinality of a minimum cyclic edge-cut of G. We call a graph super cyclically edge-connected, if the removal of any minimum cyclic edge-cut results in a component which is a shortest cycle. In this paper, we show that a connected vertex-transitive or edge-transitive graph is super cyclically edge-connected if either G is cubic with girth g(G)驴7, or G has minimum degree 驴(G)驴4 and girth g(G)驴6.