On the Metric Dimension of Imprimitive Distance-Regular Graphs
نویسندگان
چکیده
منابع مشابه
On the metric dimension of imprimitive distance-regular graphs
A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. Much attention has been paid to the metric dimension of distance-regular graphs. Work of Babai from the early 1980s yields general bounds on the metric dimens...
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A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. A graph is distance-regular if, for any two vertices u, v at each distance i, the number of neighbours of v at each possible distance from u (i.e. i−1, i or i...
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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: Annals of Combinatorics
سال: 2016
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-016-0334-9