The secure domination problem in cographs

Let G = (V, E) be a graph. A subset D of vertices of G is called a dominating set of G if for every u epsilon V \ D, there exists a vertex v epsilon D such that uv epsilon E. A dominating set D of a graph G is called a secure dominating set of G if for every u epsilon V \ D, there exists a vertex V epsilon D such that uv epsilon E and (D \ {v}) boolean OR {u} is a dominating set of G. The secure domination number of G, denoted by gamma(s)(G), is the minimum cardinality of a secure dominating set of G. In this paper, we present an 0 (n + m) time algorithm to compute the secure domination number of a cograph having n vertices and m edges. (C) 2019 Elsevier B.V. All rights reserved.