Characterization of Disconnected Two-cyclic Graphs with a Self Vertex Switching

By : G. Sumathy

Page No: 123-140

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, both connected and disconnected unicyclic graphs and connected two-cyclic graphs are characterized, each with a self vertex switching. In this paper, we characterize disconnected two-cyclic graphs with a self vertex switching.

Authors :
C. Jayasekaran : Department of Mathematics Pioneer Kumaraswamy College, Nagercoil – 629 003 
G. Sumathy : Department of Mathematics, Sree Ayyappa College for Women, Nagercoil – 629 003, India