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arXiv · 2311.01733

Independent domination stability in graphs

Saeid Alikhani·Mazharodin Mehraban·Alexei Zakharov·Hamidreza Golmohammadi
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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.

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Saeid Alikhani, Mazharodin Mehraban, Alexei Zakharov, Hamidreza Golmohammadi. 2023-11-03. Independent domination stability in graphs. https://arxiv.org/abs/2311.01733

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