A simple algorithm for secure domination in proper interval graphs

Abstract In [Secure domination in proper interval graphs, Discrete Applied Mathematics 247 (2018) 70–76], Araki and Miyazaki proposed a linear-time algorithm for finding the secure domination number of proper interval graphs. However, the example they provided is exactly a counterexample. Based on their main idea, we propose a new simple algorithm for solving this problem in this paper.