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arXiv · 1205.0327

Uniquely dimensional graphs

Behrooz Bagheri·Mohsen Jannesari·Behnaz Omoomi
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Abstract

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.

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BibTeXRIS

Behrooz Bagheri, Mohsen Jannesari, Behnaz Omoomi. 2012-05-02. Uniquely dimensional graphs. https://arxiv.org/abs/1205.0327

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