A Characterization of 2-Vertex Self Switching of Connected Unicyclic Graphs

Abstract

A graph  is created from G by eliminating all edges between  and its complement  and any non-edges between  and  are added as edges for a simple graph G(V, E) and a non empty subset . We write  for  when S={v}, and the associated switching is referred to as vertex switching. -vertex switching is another name for it. 2-vertex switching occurs when  equals 2. If B is connected and maximal, a joint at ? in G is a subgraph of G that includes G[?]. If B is connected, we refer to it as a c ; otherwise, we refer to it as a d . An acyclic graph is one that has no cycles. The term "tree" refers to a linked acyclic network. In this article, we characterize 2-vertex self switching for connected unicyclic graphs.