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

Ortega, Marivir; Isla, Rowena T.

doi:10.29020/nybg.ejpam.v13i4.3812

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2021

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“…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.…”

Section: Introductionmentioning

confidence: 99%

On k-Fair Total Domination in Graphs

Bent-Usman

Isla²

2021

Eur. J. Pure Appl. Math.

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Let G = (V (G), E(G)) be a simple non-empty graph. For an integer k ≥ 1, a k-fairtotal dominating set (kf td-set) is a total dominating set S ⊆ V (G) such that |NG(u) ∩ S| = k for every u ∈ V (G)\S. The k-fair total domination number of G, denoted by γkf td(G), is the minimum cardinality of a kf td-set. A k-fair total dominating set of cardinality γkf td(G) is called a minimum k-fair total dominating set or a γkf td-set. We investigate the notion of k-fair total domination in this paper. We also characterize the k-fair total dominating sets in the join, corona, lexicographic product and Cartesian product of graphs and determine the exact values or sharpbounds of their corresponding k-fair total domination number.

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Section: Introductionmentioning

confidence: 99%