An O(n plus m) time algorithm for computing a minimum semitotal dominating set in an interval graph

Let G = ( V, E) be a graph without isolated vertices. A set D subset of V is said to be a dominating set of G if for every vertex v is an element of V \ D, there exists a vertex u is an element of D such that uv is an element of E. A set D subset of V is called a semitotal dominating set of G if D is a dominating set and every vertex in D is within distance 2 from another vertex of D. For a given graph G, the semitotal domination problem is to find a semitotal dominating set of G with minimum cardinality. The decision version of the semitotal domination problem is shown to be NP-complete for chordal graphs and bipartite graphs. Henning and Pandey (Theor Comput Sci 766:46-57, 2019) proposed an O(n(2)) time algorithm for computing a minimum semitotal dominating set in interval graphs. In this paper, we show that for a given interval graph G = (V, E), a minimum semitotal dominating set of G can be computed in O(n + m) time, where n = |V| and m = | E|. This improves the complexity of the semitotal domination problem for interval graphs from O(n(2)) to O(n + m).