Edge-superconnectivity of semiregular cages with odd girth

Abstract

A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a $\{d,d+1\}$ **image** -semiregular graph if all its vertices have degree either d or $d+1$ **image** . A smallest $\{d,d+1\}$ **image** -semiregular graph G with girth g is said to be a $(\{d,d+1\};g)$ **image** -cage. We show that every $(\{d,d+1\};g)$ **image** -cage with odd girth g is edge-superconnected. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011 © 2011 Wiley Periodicals, Inc.