2025/08/14 by Pedrano, Ariel C., Paluga, Rolando N.
#54C05 #54C08 #54C10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.10952
Let G be a connected graph. A non-empty T⊆ V(G) is a 2-movable total dominating set of G if T is a total dominating set and for every pair x,y ∈ T, T \backslash \x, y\ is a total dominating set in G, or there exist u, v ∈ V(G) \backslash T such that u and v are adjacent to x and y, respectively, and (T \backslash \x,y\) ∪ \u,v\ is a total dominating set in G. The 2-movable total domination number of G, denoted by γmt2(G), is the minimum cardinality of a 2-movable total dominating set of G. A 2-movable total dominating set with cardinality equal to γmt2(G) is called γmt2-set of G. This paper present the 2-movable total domination in the join and corona of graphs.