Elsevier

Discrete Mathematics

Volume 310, Issues 17–18, 28 September 2010, Pages 2273-2279
Discrete Mathematics

On super restricted edge-connectivity of edge-transitive graphs

https://doi.org/10.1016/j.disc.2010.04.024Get rights and content
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Abstract

Let X=(V,E) be a connected graph. Then X is called super restricted edge-connected, in short, sup-λ, if every minimum edge set F of X such that XF is disconnected and every component of XF has at least two vertices, the set of edges being adjacent to a certain edge with minimum edge degree in X. In this paper, by studying the λ-superatoms of X, we characterize super restricted edge-connected edge-transitive graphs. As a corollary, we present a sufficient and necessary condition for connected vertex-transitive line graphs to be super vertex-connected.

Keywords

Vertex-transitive graphs
Edge-transitive graphs
Restricted edge-connectivity
Super restricted edge-connectivity
Line graphs

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The research is supported by NSFC (No. 10671165), NSFXJ (No. 2010211A06) and XJEDU (No. 2004G05).