Strong Hotspot Domination Integrity of Corona Products, Comb Products and Shadow Graphs with Applications
Year: 2026
Type: article
Abstract: The study of graph vulnerability parameters provides valuable insights into the structural stability and resilience of networks when there is a disruption. The strong hotspot domination integrity ( $$DI_{SH}$$ ) is one such measure, combining domination, integrity, and heatmap centrality into a single context that captures both control and resilience of a network. It is defined as $$DI_{SH}(G)=\min \{|S_{SH}|+m(G-S_{SH}): S_{SH}\}$$ and the parameter is taken over all strong hotspot dominating sets $$S_{SH}$$ , where domination is governed by the heatmap centrality condition ensuring that for every vertex $$u\in V(G)-S_{SH}$$ , there exists $$v\in S_{SH}$$ such that $$HC(v)\ge HC(u)$$ . In this paper, we investigate the strong hotspot domination integrity for three important graph operations: the corona product, the shadow graph, and the comb product of certain graphs and understand how the parameter behaves under structural transformations. Moreover, we present few applications of strong hotspot domination integrity in acupuncture, electric power networks, and medicine.
Authors: Annie Clare Antony, V. Sangeetha
Institution: Christ University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,190
OpenAlex ID: W7204040126