On 2-Movable Domination in the Join and Corona of Graphs

2025/08/20 by Pedrano, Ariel C., Paluga, Rolando N.
#54C08 #54C10 #: 54C05 #FOS: Mathematics #G.2 #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2509.05301

Abstract

Let G be a connected graph. A non-empty S⊆ V(G) is a 2-movable dominating set of G if S is a dominating set and for every pair x,y ∈ S, S\backslash \x, y\ is a dominating set in G, or there exist u, v ∈ V(G) \backslash S such that u and v are adjacent to x and y, respectively, and (S \backslash \x,y\) ∪ \u,v\ is a dominating set in G. The 2-movable domination number of G, denoted by γ_m²(G), is the minimum cardinality of a 2-movable dominating set of G. A 2-movable dominating set with cardinality equal to γ_m²(G) is called γ_m²-set of G. This paper present the 2-movable domination number in the corona and join of graphs.

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