FAIR TOTAL DOMINATION NUMBERIN CACTUS GRAPHS

Nader Jafari Rad | M. Hajian

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=116573
Date :  2019/05/29
Publish in :    Discussiones Mathematicae Graph Theory

Link :  https://www.dmgt.uz.zgora.pl/publish/view_pdf.php?ID=7076
Keywords :fair total domination, cactus graph.

Abstract :

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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 ftdk(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 of a nonempty graph G, denoted by ftd(G), of G is the minimum cardinality of an FTD-set in G. In this paper, we present upper bounds for the 1-fair total domination number of cactus graphs, and characterize cactus graphs achieving equality for the upper bounds.