Fair total domination in the join, corona, and composition of graphs

Abstract

In this paper, we characterize the fair total dominating sets in the join and corona of graphs and determine the corresponding fair total domination numbers. We also characterize some fair total dominating sets in the composition of graphs and give sharp upper bounds for the corresponding fair total domination numbers.

On k-Fair Total Domination in Graphs

“…Maravilla et al [4] introduced the notion of k-fair total domination in graphs. For a non-empty graph G and an integer k ≥ 1, a k-fair total dominating set (kf td-set) is a total dominating set S ⊆ V (G) such that |N G (u) ∩ S| = k for every u ∈ V (G)\S.…”

Fair total domination number in cactus graphs

“…Maravilla et al [13] introduced the concept of fair total domination in graphs. For an integer k ≥ 1 and a graph G with no isolated vertex, a k-fair total dominating set, abbreviated kFTD-set, is a total dominating set S ⊆ V (G) such that |N (u)∩S| = k for every u ∈ V (G)\S.…”