Metric dimension of symplectic dual polar graphs and symmetric bilinear forms graphs
نویسندگان
چکیده
منابع مشابه
Metric dimension of dual polar 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 μ(Γ) is the smallest size of a resolving set for Γ. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R of the incidence matrix of the corresponding polar spac...
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In [R.F. Bailey, K. Meagher, On the metric dimension of Grassmann graphs, arXiv:1010.4495 ], Bailey and Meagher obtained an upper bound on the metric dimension of Grassmann graphs. In this note we show that qn+d−1+⌊ d+1 n ⌋ is an upper bound on the metric dimension of bilinear forms graphs Hq(n, d)when n ≥ d ≥ 2. As a result, we obtain an improvement on Babai’s most general bound for the metric...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.09.023