2-power domination number for Knödel graphs and its application in communication networks

¹ Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India
² Department of Mathematics, Rajalakshmi Engineering College, Thandalam 602105, India
³ Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai 602105, India

^* Corresponding author: arulanand7875@gmail.com

Received: 1 November 2022
Accepted: 1 November 2023

Abstract

In a graph G, if each node v ∈ V(G) \ S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γ_p,k(G). In this paper, we have obtained the 2-power domination number represented by γ_p,2(G) for 4-regular Knödel graphs and given the lower bound for 5-regular Knödel graphs.