Fair total domination number in cactus graphs | Zendy

Majid Hajian | Zendy; Nader Jafari Rad | Zendy

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Fair total domination number in cactus graphs

Author(s) -

Majid Hajian,

Nader Jafari Rad

Publication year - 2019

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2225

Subject(s) - dominating set , domination analysis , combinatorics , mathematics , vertex (graph theory) , graph , cardinality (data modeling) , cactus , discrete mathematics , set (abstract data type) , computer science , biology , botany , data mining , programming language

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.

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