Neighborhood Connected k-Fair Domination Under Some Binary Operations

Wardah Masanggila Bent-Usman, Rowena Isla, Sergio Canoy


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.

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