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Zou et al. (2019) proposed an algorithm for calculating a minimum secure dominating set of a proper interval graph. However, we find a counterexample for which the algorithm outputs an incorrect subset of vertices. In this paper, we provide a modified algorithm and the proofs for the correctness. [ABSTRACT FROM AUTHOR]

A set S ⊂ V is a co-secure dominating set of a graph G = (V , E) if S is a dominating set, and for each u ∈ S there exists a vertex v ∈ V ∖ S such that u v ∈ E and (S ∖ { u }) ∪ { v } is a dominating set. Note that | V | > 1. The minimum cardinality of a co-secure dominating set in G is the co-secure domination number of G. In this paper, we propose a linear-time algorithm for finding the co-secure domination number of proper interval graphs. [ABSTRACT FROM AUTHOR]