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The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $\\beta(G)$. In this paper, we prove that in a connected graph $G$ of order $n$, $\\beta(G)\\leq n-\\gamma(G)$, where $\\gamma(G)$ is the domination number of $G$, and the equality holds if and only if $G$ is a complete graph or a complete bipartite graph $K_{s,t}$, $ s,t\\geq 2$. 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