An algorithm for the secure total domination problem in proper interval graphs

Abstract

A subset S of vertices of G is a total dominating set if, for any vertex v, there is a vertex in S adjacent to v. A total dominating set S is a secure total dominating set if, for any vertex v∉S, there is a vertex u∈S such that uv is an edge and (S∖{u})∪{v} is also a total dominating set. In this paper, we design an O(m)-time algorithm for computing a minimum secure total dominating set in a proper interval graph, where m is the number of edges.