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Resolvability in Subdivision of Circulant Networks

Author

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  • Jianxin Wei
  • Syed Ahtsham Ul Haq Bokhary
  • Ghulam Abbas
  • Muhammad Imran

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.

Suggested Citation

  • Jianxin Wei & Syed Ahtsham Ul Haq Bokhary & Ghulam Abbas & Muhammad Imran, 2020. "Resolvability in Subdivision of Circulant Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-11, September.
    • Handle: RePEc:hin:jnddns:4197678
    DOI: 10.1155/2020/4197678
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    Cited by:

    1. Kühl, Carl & Bourlakis, Michael & Aktas, Emel & Skipworth, Heather, 2022. "Product-service systems and circular supply chain practices in UK SMEs: The moderating effect of internal environmental orientation," Journal of Business Research, Elsevier, vol. 146(C), pages 155-165.
    2. McDougall, Natalie & Wagner, Beverly & MacBryde, Jill, 2022. "Competitive benefits & incentivisation at internal, supply chain & societal level circular operations in UK agri-food SMEs," Journal of Business Research, Elsevier, vol. 144(C), pages 1149-1162.

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