Some results on strong 2 - vertex duplication self switching of some connected graphs

Abstract

A vertex \(v \in V(G)\) is said to be a self vertex switching of \(G\) if \(G\) is isomorphic to \(G^v\), where \(G^v\) is the graph obtained from \(G\) by deleting all edges of \(G\) incident to \(v\) in \(G\) and adding all edges incident to \(v\) which are not in \(G\). A vertex \(v^{\prime}\) is the duplication of \(v\) if all the vertices which are adjacent to \(v\) in \(G\) are also adjacent to \(v^{\prime}\) in \(D(v G)\), which is the duplication graph of \(G\). Duplication self vertex switching of various graphs are given in the literature. In this paper we discuss about the 2-vertex duplication self switching graphs.