Complexity and bounds for disjunctive total bondage

Abstract

A subset S subset of V(G) is a disjunctive total dominating set if each vertex has a neighbor in S or has at least two vertices in Sat distance two from it. The disjunctive total domination number gamma(d)(t)(G) is the minimum cardinality of a disjunctive total dominating set in G. Disjunctive total bondage number, b(t)(d)(G), of a graph G with no isolated vertex is defined as the minimum cardinality of edge set B subset of E(G) whose deletion obtains a graph G - B with no isolated vertex satisfying gamma(d)(t)(G - B) > gamma(d)(t)(G). If there is no such set B, it is then defined as b(t)(d)(G) = infinity. We, in this paper, present some bounds on disjunctive total bondage. Also, we prove that the disjunctive total bondage problem is NP-complete, even for bipartite graphs. (C) 2021 Elsevier B.V. All rights reserved.