Total domination stability in graphs

Disjunctive total domination stability in graphs

“…For the total domination stability, Henning et al 18 observe (1) of the following result by considering K 0 .…”

“…(b) If diam(G) ≥ 3, then there is a d t (G)-set which contains no leaf of G. The term unique graph, which is mentioned in the paper of Bauer et al 16 and has no vertices, is called the null graph K 0 by Henning et al 18 Since the domination number of a null graph is zero, the following bound is given by Rad et al:…”

“…Bauer et al 16 introduced the concept of domination stability in graphs, and then Rad et al 17 continued to study this parameter. After then, the total version of it was introduced by Henning and Krzywkowski 18 . A graph which has no isolated vertex is an isolate‐free graph .…”

“…After then, the total version of it was introduced by Henning and Krzywkowski. 18 A graph which has no isolated vertex is an isolate-free graph. For an isolate-free graph G, a set S ⊆ V(G) is a non-isolating set of vertices in G if G − S is an isolate-free graph, in which G − S is the graph obtained from G by deleting vertices of S and all edges incident to vertices in S. The total domination stability is defined as the minimum size of a non-isolating set of vertices in G whose removal changes (increases, + t -stability of G, or decreases, − t -stability of G) the total domination number.…”

Paired domination stability in graphs

“…Stability for other domination type parameters has been studied in the literature. For example, total domination stability, 2-rainbow domination stability, exponential domination stability, Roman domination stability are studied in [1,2,12,15,16], among other papers. In this paper we study the paired version of domination stability.…”