Graph-theoretic analysis demonstrates secure point set domination parameters and bounds in Mycielskian graphs, highlighting new structural safeguards for networks.
Let [Formula: see text] be a simple graph. A dominating set [Formula: see text] is called secure if for any [Formula: see text] in [Formula: see text] there exists [Formula: see text] such that [Formula: see text] is a dominating set of [Formula: see text] [9]. A dominating set [Formula: see text] is called rigid secure if for any [Formula: see text] there exists a unique [Formula: see text] such that [Formula: see text] is a dominating set of [Formula: see text] In this paper, we introduce and investigate two new parameters, namely the secure point set domination number and the rigid secure point set domination number. Furthermore, for the Mycielskian of a graph, bounds for the secure point set domination number are established. The results presented in this article are different from those reported by Purnima Gupta and Alka Goyal [1].
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Sumathi et al. (2026) studied this question.
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