Uniquely dimensional graphs
  A set $W\subseteq V(G)$ is called a resolving set, if for each two distinct vertices $u,v\in V(G)$ there exists $w\in W$ such that $d(u,w)\neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis.   A graph with a unique metric basis is called a uniquely dimensional graph.   In this paper, we study some properties of uniquely dimensional graphs. 
Behrooz Bagheri, Mohsen Jannesari and Behnaz Omoomi
math.CO