# 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 (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

M. Hajian, N. Jafari Rad

Title:

A note on the fair domination number in outerplanar graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-11-14, Revised: 2018-07-02, Accepted: 2018-07-02, https://doi.org/10.7151/dmgt.2157

Abstract:

For $k\geq 1$, a $k$-fair dominating set (or just $k$FD-set), in a graph $G$ is a dominating set $S$ such that $|N(v)\cap S| = k$ for every vertex $v\in V- S$. The $k$-fair domination number of $G$, denoted by $fd_k(G)$, is the minimum cardinality of a $k$FD-set. A fair dominating set, abbreviated FD-set, is a $k$FD-set for some integer $k\geq 1$. The fair domination number, denoted by $fd(G)$, of $G$ that is not the empty graph, is the minimum cardinality of an FD-set in $G$. In this paper, we present a new sharp upper bound for the fair domination number of an outerplanar graph.

Keywords:

fair domination, outerplanar graph, unicyclic graph