Abstract
A subset S⊆V(G) is a disjunctive total dominating set if each vertex has a neighbor in S or has at least two vertices in S at distance two from it. The disjunctive total domination numberγtd(G) is the minimum cardinality of a disjunctive total dominating set in G. Disjunctive total bondage number, btd(G), of a graph G with no isolated vertex is defined as the minimum cardinality of edge set B⊆E(G) whose deletion obtains a graph G−B with no isolated vertex satisfying γtd(G−B)>γtd(G). If there is no such set B, it is then defined as btd(G)=∞. 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.
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