ON 2-MOVABLE DOMINATION IN THE JOIN AND CORONA OF GRAPHS

Abstract

Let $G$ be a connected graph. Then 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 $x, y \in S, S-\{x, y\}$ 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 $\gamma_m^2(G)$, is the minimum cardinality of a 2-movable dominating set of G. A 2-movable dominating set with cardinality equal to $\gamma_m^2(G)$ is called $\gamma_m^2$-set of $G$.

This paper obtains 2-movable domination numbers for the corona and join of graphs.

Received: January 23, 2024;
Revised: September 28, 2024;
Accepted: November 20, 2024