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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05301 |
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Table of Contents:
- Let $G$ be a connected graph. A non-empty $S\subseteq V(G)$ is a $2$-movable dominating set of $G$ if $S$ is a dominating set and for every pair $x,y \in S$, $S\backslash \{x, y\}$ is a dominating set in $G$, or there exist $u, v \in V(G) \backslash S$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(S \backslash \{x,y\}) \cup \{u,v\}$ is a dominating set in $G$. The $2$-movable domination number of $G$, denoted by $γ_{m}^{2}(G)$, is the minimum cardinality of a 2-movable dominating set of $G$. A 2-movable dominating set with cardinality equal to $γ_{m}^{2}(G)$ is called $γ_{m}^{2}$-set of $G$. This paper present the 2-movable domination number in the corona and join of graphs.