A graph $G$ of order $n$ is said to be $\Sigma^{'}$ labeled if there exist a bijection $f:V(G)\rightarrow [n]$ and a constant $c$ such that for all $v\in V(G)$, $\sum_{u\in N[v]} f(u)=c$. The uniqueness of the constant $c$ has been an open question that was posed by Prof. Arumugam at the 2010 IWOGL Conference in Duluth. The question of the uniqueness of such a constant can be extended to arbitrary neighborhoods and to arbitrary sets of labels. For a set $D\subset \mathbb{N}$, let $N_D(v)=\{u\in V(G):d(u,v)\in D\}$, and let $W$ be a multiset of real numbers. Graph $G$ is said to be $(D,W)$-vertex magic if there exists a bijection $g:V(G)\rightarrow W$ such that for all $v\in V(G)$, $\sum_{u\in N_D(v)}g(u)$ is a constant, called the $(D,W)$-vertex magic constant. In this paper we prove that, even for these more general conditions, a $(D,W)$-vertex magic constant will be unique. Moreover, the constant can be determined using a generalization of the fractional domination number of the graph.