Bounds on the fair total domination number in trees and unicyclic graphs

Majid Hajian, Nader Jafari Rad, Lutz Volkmann
2019 The Australasian Journal of Combinatorics  
For k ≥ 1, a k-fair total dominating set (or just kFTD-set) in a graph G is a total dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V −S. The k-fair total domination number of G, denoted by f td k (G), is the minimum cardinality of a kFTD-set. A fair total dominating set, abbreviated FTD-set, is a kFTD-set for some integer k ≥ 1. The fair total domination number, denoted by f td(G), of G that is not the empty graph, is the minimum cardinality of an FTD-set in G. In this paper, we
more » ... present upper bounds for the fair total domination number of trees and unicyclic graphs, and characterize trees and unicyclic graphs achieving equality for the upper bounds.
dblp:journals/ajc/HajianRV19 fatcat:26yno5dyobh6tlwrbloxu75wmu