Generalization of IP Domination Number for Complement Graphs

Objectives: This research introduces Isolate Pendant domination parameter, a novel concept applied to complement graphs. Methods: This investigation explores Isolate Pendant domination in complement graphs, characterizing the minimum dominating set and satisfying isolate pendant domination conditions within induced graphs, by applying this parameter in −𝐺 to yield insightful results. Findings: This study determines the minimum Isolate Pendant Dominating set (IPD-set) in complement graphs, characterizing exact values for complement graphs. Moreover, generalized results are derived for complement graphs. Novelty: This study pioneers new insights into the behavior of complement graphs, presenting exact values and results on the Isolate Pendant domination number, thereby making a profound impact on the advancement of graph theory. Keywords: Isolate vertex; Pendant vertex; Complement graphs; IPDominatingset; IPdominationnumber.