Disjunctive total domination stability in graphs

Abstract

A setS subset of V(G) is a disjunctive total dominating set ofGif every vertex has a neighbor inSor has at least two vertices inSat 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 ofGas the minimum size of a non-isolating set of vertices inGwhose 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.