Disjunctive total domination stability in graphs

Abstract

A set S⊆V(G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance two from it. The minimum cardinality of such a set is equal to the disjunctive total domination number. A non‐isolating set of vertices of a graph is a set whose removal forms a graph with no isolated vertex. We define the disjunctive total domination stability of G as the minimum size of a non‐isolating set of vertices in G whose removal changes (increases or decreases) the disjunctive total domination number. In this paper, we determine the exact values of disjunctive total domination stability of some special graphs and some trees. Moreover, we give some properties about vertices that change the disjunctive total domination number.