On Semitotal k-Fair and Independent k-Fair Domination in Graphs

Marivir Ortega, Rowena Isla

Abstract

In this paper, we introduce and investigate the concepts of semitotal k-fair domination and independent k-fair domination, where k is a positive integer. We also characterize the semitotal 1-fair dominating sets and independent k-fair dominating sets in the join, corona, lexicographic product, and Cartesian product of graphs and determine the exact value or sharp bounds of the corresponding semitotal 1-fair domination number and independent k-fair domination number.

Keywords

Semitotal domination, Independent domination, $k$-Fair domination, Join, Corona, Lexicographic product, Cartesian product

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