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Rodriguez-Velazquez, Magdalena Lemanska","submitted_at":"2011-10-24T17:38:27Z","abstract_excerpt":"Given an ordered partition $\\Pi =\\{P_1,P_2, ...,P_t\\}$ of the vertex set $V$ of a connected graph $G=(V,E)$, the \\emph{partition representation} of a vertex $v\\in V$ with respect to the partition $\\Pi$ is the vector $r(v|\\Pi)=(d(v,P_1),d(v,P_2),...,d(v,P_t))$, where $d(v,P_i)$ represents the distance between the vertex $v$ and the set $P_i$. A partition $\\Pi$ of $V$ is a \\emph{resolving partition} of $G$ if different vertices of $G$ have different partition representations, i.e., for every pair of vertices $u,v\\in V$, $r(u|\\Pi)\\ne r(v|\\Pi)$. 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