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On the partition dimension of unicyclic graphs | | Juan A. Rodriguez-Velazquez
; Ismael G. Yero
; Henning Fernau
; | | Date: |
15 Nov 2011 | | 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} if different vertices of $G$ have different
partition representations, i.e., for every pair of vertices $u,vin V$,
$r(u|Pi)
e r(v|Pi)$. The emph{partition dimension} of $G$ is the minimum
number of sets in any resolving partition for $G$. In this paper we obtain
several tight bounds on the partition dimension of unicyclic graphs. | | Source: | arXiv, 1111.3513 | | Services: | Forum | Review | PDF | Favorites | |
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