On k-Fair Total Domination in Graphs

Authors

  • Wardah Masanggila Bent-Usman Mindanao State University-Main Campus
  • Rowena T. Isla

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i2.3967

Abstract

Let G = (V (G), E(G)) be a simple non-empty graph. For an integer k ≥ 1, a k-fair
total 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 sharp
bounds of their corresponding k-fair total domination number.

Author Biography

Wardah Masanggila Bent-Usman, Mindanao State University-Main Campus

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How to Cite

Bent-Usman, W. M., & Isla, R. T. (2021). On k-Fair Total Domination in Graphs. European Journal of Pure and Applied Mathematics, 14(2), 578–589. https://doi.org/10.29020/nybg.ejpam.v14i2.3967