Journal Title
Title of Journal: Bull Malays Math Sci Soc
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Abbravation: Bulletin of the Malaysian Mathematical Sciences Society
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Publisher
Springer Singapore
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Authors: Weihua Yang Chengfu Qin Meirun Chen
Publish Date: 2015/12/11
Volume: 39, Issue: 1, Pages: 13-27
Abstract
A cyclic edgecut of a graph G is an edge set the removal of which separates two cycles If G has a cyclic edgecut then it is said to be cyclically separable For a cyclically separable graph G the cyclic edgeconnectivity lambda cG is the cardinality of a minimum cyclic edgecut of G Let zeta G=min omega X X text induce text a text shortest text cycle text in G where omega X is the number of edges with one end in X and the other end in VGX A cyclically separable graph G with lambda cG=zeta G is said to be cyclically optimal In particular we call a graph G super cyclically edgeconnected if every minimum cyclic edgecut isolates a shortest cycle of G In this work we first discuss the cyclic edgeconnectivity of vertex transitive graphs regular doubleorbit graphs and the doubleorbit graphs with two orbits of same size moreover we also discuss the supercyclic edgeconnectivity of doubleorbit graphs mentioned above
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