Super cyclically edge connected transitive graphs

Zhao Zhang () and Bing Wang
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Zhao Zhang: Xinjiang University
Bing Wang: Xinjiang University

Journal of Combinatorial Optimization, 2011, vol. 22, issue 4, No 6, 549-562

Abstract: 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 λ 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)≥7, or G has minimum degree δ(G)≥4 and girth g(G)≥6.

Keywords: Cyclic edge-cut; Cyclic edge-connectivity; Super cyclically edge-connected; Vertex-transitive; Edge-transitive (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-010-9304-z

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