Abstract
A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd graphs, doubled Grassmann graphs and twisted Grassmann graphs, respectively, and obtain the upper bounds on the metric dimension of these graphs.
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Acknowledgements
This research is partially supported by NSF of Hebei Province, TPF-2011-11 of Hebei Province, NSF of China (10971052, 10871027), NCET-08-0052, Langfang Teachers’ College (LSZB201104), Hunan Provincial Natural Science Foundation of China (09JJ3006), and the Fundamental Research Funds for the Central Universities of China.
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Guo, J., Wang, K. & Li, F. Metric dimension of some distance-regular graphs. J Comb Optim 26, 190–197 (2013). https://doi.org/10.1007/s10878-012-9459-x
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DOI: https://doi.org/10.1007/s10878-012-9459-x