Correcting the algorithm for the secure domination number of cographs by Jha, Pradhan, and Banerjee

TL;DR

This paper identifies and corrects an incomplete lemma in a previous linear algorithm for computing the secure domination number of cographs, ensuring the algorithm's correctness and maintaining its linear complexity.

Contribution

It provides a corrected lemma and demonstrates that the modified algorithm retains linear complexity for computing the secure domination number of cographs.

Findings

The original lemma was incomplete.

The corrected lemma ensures algorithm correctness.

The algorithm's linear complexity is preserved.

Abstract

Jha, Pradhan, and Banerjee devised a linear algorithm to compute the secure domination number of a cograph. Here it is shown that their Lemma~2, which is crucial for the computational complexity of the algorithm, is incomplete. An accordingly modified lemma is proved and it is demonstrated that the complexity of the modified algorithm remains linear.