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}-semiregular graph if all its vertices have degree either d or d+1. A smallest {d,d+1}-semiregular graph G with girth g is said to be a ({d,d+1};g)-cage. We show that every ({d,d+1};g)-cage with odd girth g is edge-superconnected. Copyright © 2011 Wiley Periodicals, Inc.