Neighborhood Connected k-Fair Domination Under Some Binary Operations

Abstract

Let G=(V(G),E(G)) be a simple graph. A neighborhood connected k-fair dominating set (nckfd-set) is a dominating set S subset V(G) such that |N(u) intersection S|=k for every u is an element of V(G)\S and the induced subgraph of S is connected. In this paper, we introduce and invistigate the notion of neighborhood connected k-fair domination in graphs. We also characterize such dominating sets in the join, corona, lexicographic and cartesians products of graphs and determine the exact value or sharp bounds of their corresponding neighborhood connected k-fair domination number.

On k-Fair Total Domination in Graphs

“…In 2014, Maravilla et al [5] characterized the k-fair dominating sets in the join, corona, lexicographic product, and Cartesian product of graphs and determined the bounds or exact values of the k-fair domination numbers of these graphs. Two variants of k-fair domination, namely connected k-fair domination and neighborhood connected k-fair domination, were studied by Bent-Usman et al [1,6] in 2018 and 2019, respectively. Recently, Ortega and Isla [7] introduced and investigated the concepts of semitotal k-fair domination and independent k-fair domination in graphs.…”