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- W2057621845 abstract "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 $vin V$ 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 $u,vin V$, $r(u|Pi)ne r(v|Pi)$. The emph{partition dimension} of $G$ is the minimum number of sets in any resolving partition of $G$. In this paper we obtain several tight bounds on the partition dimension of trees." @default.
- W2057621845 created "2016-06-24" @default.
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- W2057621845 date "2014-03-01" @default.
- W2057621845 modified "2023-10-18" @default.
- W2057621845 title "On the partition dimension of trees" @default.
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- W2057621845 doi "https://doi.org/10.1016/j.dam.2013.09.026" @default.
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