Interchange similar self vertex switchings in graphs

Abstract

A vertex v ∈ V(G) is said to be a self vertex switching of G if G is isomorphic to Gv , where Gv is the graph obtained from G by deleting all edges of G incident to v and adding all edges incident to v which are not in G. Two vertices u and v in G are said to be interchange similar if there exists an automorphism α of G such that α(u) = v and α(v) = u. In this paper, we give a sufficient condition for a self vertex switching to be interchange similar with another vertex.