The metric dimension of Cayley digraphs
نویسندگان
چکیده
منابع مشابه
The partition dimension of Cayley digraphs
Let G be a (di)graph and S a set of vertices of G. We say S resolves two vertices u and v of G if d(u, S) 6= d(v, S). A partition Π = {P1, P2, . . . , Pk} of V (G) is a resolving partition of G if every two vertices of G are resolved by Pi for some i (1 ≤ i ≤ k). The smallest cardinality of a resolving partition of G, denoted by pd(G), is called the partition dimension of G. A vertex r of G res...
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A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.09.015