The Metric Dimension of Some Generalized Petersen Graphs

Zehui Shao, S. M. Sheikholeslami, Pu Wu and Jia-Biao Liu

Discrete Dynamics in Nature and Society, 2018, vol. 2018, 1-10

Abstract:

The distance between two distinct vertices and in a graph is the length of a shortest -path in . For an ordered subset of vertices and a vertex in , the code of with respect to is the ordered -tuple . The set is a resolving set for if every two vertices of have distinct codes. The metric dimension of is the minimum cardinality of a resolving set of . In this paper, we first extend the results of the metric dimension of and and study bounds on the metric dimension of the families of the generalized Petersen graphs and . The obtained results mean that these families of graphs have constant metric dimension.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4531958

DOI: 10.1155/2018/4531958

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