Changing and Unchanging the Domination Number of a Graph

Abstract

A dominating set in a graph $G$ is a set $D$ of nodes such that every node of $G$ is either in $D$ or is adjacent to some node in $D$. The domination number $\alpha (G)$ is the minimum size of a dominating set. The purpose of this paper is to explore the changing or unchanging of $\alpha (G)$ when either a node is deleted, or an edge is added or deleted.