Self Vertex Switching of Connected Two-Cyclic 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. A graph G is called a two-cyclic graph if it has exactly two cycles. Trees, forests and both connected and disconnected unicyclic graphs are characterized, each with a self vertex switching. In this paper, we characterize connected two-cyclic graphs with a self vertex switching.