Mohsen Jannesari, Behnaz Omoomi, Mathematics Department, Isfahan University of Technology, Isfahan, 84156-83111, Iran, e-mail: m.jannesari@math.iut.ac.ir; bomoomi@cc.iut.ac.ir
Abstract: For an ordered set $W=\{w_1,w_2,\ldots,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),\ldots,d(v,w_k))$ is called the metric representation of $v$ with respect to $W$, where $d(x,y)$ is the distance between vertices $x$ and $y$. A set $W$ is called a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. The minimum cardinality of a resolving set for $G$ is its metric dimension. In this paper, we characterize all graphs of order $n$ with metric dimension $n-3$.
Keywords: resolving set; basis; metric dimension
Classification (MSC 2010): 05C12
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