We introduce the notion of uniform number of a graph. The uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a
constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$
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