Abstract
A set D of vertices in an isolate-free graph G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2 of another vertex of D. The semitotal domination number of G is the minimum cardinality of a semitotal dominating set of G. The semitotal domination subdivision number sd γ t2 (G) of G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the semitotal domination number of G. In this paper, we initiate the study of semitotal domination subdivision number. We first show that the decision problem for the semitotal domination subdivision number is NP-complete even for bipartite graphs, and then establish bounds on the semitotal domination subdivision number for some families of graphs.
Published Version
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