Restrained dr-Power Dominating Sets in Graphs
Isagani S. Cabahug, Jr. *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Rolito G. Eballe
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Cherry Mae R. Balingit
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Consider a nontrivial connected graph G. In this context, a set R that is not empty and a subset of V (G) is referred to as a restrained dr-power dominating set of G. This means that the induced subgraph of the complement of R in G does not contain any isolated vertex and qualifies as a dr-power dominating set of G. To determine the restrained dr-power domination number of G, denoted as y*rpw (G), we look at the minimum cardinality of a restrained dr-power dominating set. This study presents significant insights into the restrained dr-power dominating set of a graph G. It provides concrete realizations and exact values for the restrained dr-power domination number within specific graph classes, such as path and cycle graphs, as well as in the context of join and corona operations. Additionally, characterizations of the restrained dr-power dominating set in the join and corona of graphs are demonstrated.
Keywords: Restrained domination, dr-power domination, restrained dr-power domination