Resolvability in Subdivision of Circulant Networks

Jianxin Wei, Syed Ahtsham Ul Haq Bokhary, Ghulam Abbas and Muhammad Imran

Discrete Dynamics in Nature and Society, 2020, vol. 2020, 1-11

Abstract:

Circulant networks form a very important and widely explored class of graphs due to their interesting and wide-range applications in networking, facility location problems, and their symmetric properties. A resolving set is a subset of vertices of a connected graph such that each vertex of the graph is determined uniquely by its distances to that set. A resolving set of the graph that has the minimum cardinality is called the basis of the graph, and the number of elements in the basis is called the metric dimension of the graph. In this paper, the metric dimension is computed for the graph constructed from the circulant graph by subdividing its edges. We have shown that, for , has an unbounded metric dimension, and for and , has a bounded metric dimension.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4197678

DOI: 10.1155/2020/4197678

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