Independent domination stability in graphs

Abstract

A non-empty set $S\subseteq V(G)$ of the simple graph $G=(V(G),E(G))$ is an independent dominating set of $G$ if every vertex not in $S$ is adjacent with some vertex in $S$ and the vertices of $S$ are pairwise non-adjacent. The independent domination number of $G$, denoted by ${\gamma }_i(G)$, is the minimum size of all independent dominating sets of $G$. The independent domination stability, or simply $id$-stability of $G$ is the minimum number of vertices whose removal changes the independent domination number of $G$. In this paper, we investigate properties of independent domination stability in graphs. In particular, we obtain several bounds and obtain the independent domination stability of some operations of two graphs.

10 pages, 2 figures