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# Article

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Keywords:
resolving set; basis; metric dimension
Summary:
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\$.
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