Self-Vertex Switchings of Disconnected Unicyclic 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 $v$ and adding all edges incident to $v$ which are not in $G$. In [6], the author characterized connected unicyclic graphs each with a self vertex switching. In this paper, we characterize disconnected unicyclic graphs each with a self vertex switching.