[Dept. of Mathematics\
University of Johannesburg\
Auckland Park 2006, South Africa\
mahenning@uj.ac.za]{}

\

[**Keywords:** Fair domination. ]{}\

Introduction
============

In this paper, we continue the study of domination in graphs. Domination in graphs is now well studied in Graph Theory. The literature on this subject has been surveyed and detailed in the two books by Haynes, Hedetniemi, and Slater [@hhs1; @hhs2]. For notation and Graph Theory terminology we in general follow [@hhs1]. Specifically, let $G = (V, E)$ be a graph with vertex set $V$ of order $n = |V|$ and edge set $E$ of size $m =
|E|$, and let $v$ be a vertex in $V$. The *open neighborhood* of $v$ is the set $N(v) = \{u \in V \, | \, uv \in E\}$, while the *closed neighborhood* of $v$ is the set $N[v] = N(v) \cup
\{v\}$.

Let $G = (V,E)$ be a graph. A *dominating set* in $G$ is a set $D$ of vertices of $G$ such that every vertex $v \in V$ is either in $D$ or adjacent to a vertex of $D$. A vertex in $D$ is said to *dominate* a vertex outside $D$ if they are adjacent in $G$. The *domination number* of 