Self vertex switchings of connected unicyclic 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. In [6], the author characterized trees each with a self vertex switching. In this paper we characterize connected unicyclic graphs each with a self vertex switching.