Paired disjunctive domination in some shadow distance graphs
Hande Tunçel Gölpek, Aysun Aytaç · Discrete Mathematics Algorithms and Applications · 2025
This paper investigates the concept of paired disjunctive domination, initially proposed by Henning et al. A subset [Formula: see text] is defined as a disjunctive dominating set of a graph [Formula: see text] if, for every vertex [Formula: see text], there exists either a vertex in [Formula: see text] adjacent to [Formula: see text], or there are at least two vertices in [Formula: see text] such that their distance from [Formula: see text] is exactly two in [Formula: see text]. Furthermore, a disjunctive dominating set [Formula: see text] is labeled as a paired disjunctive dominating set if the induced subgraph by [Formula: see text] in [Formula: see text] contains a perfect matching. This paper explores the implications of the paired disjunctive domination parameter on shadow graphs, 2-distance graphs, and 3-distance path and cycle shadow graphs.