# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

Title:

Fair total domination number in cactus graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-08-29, Revised: 2019-04-03, Accepted: 2019-04-03, https://doi.org/10.7151/dmgt.2225

Abstract:

For $k\geq 1$, a $k$-fair total dominating set (or just kFTD-set) in a graph $G$ is a total dominating set $S$ such that $|N(v)\cap S| = k$ for every vertex $v\in V {\setminus} S$. The $k$-fair total domination number of $G$, denoted by $ftd_k(G)$, is the minimum cardinality of a kFTD-set. A fair total dominating set, abbreviated FTD-set, is a kFTD-set for some integer $k\geq 1$. 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.

Keywords:

fair total domination, cactus graph