Super cyclically edge connected transitive graphs |
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Authors: | Zhao Zhang Bing Wang |
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Institution: | (2) Department of Information and Computer Systems, University of Rome, Rome, Italy |
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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 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. |
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Keywords: | |
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