Resolvability in Subdivision of Circulant Networks Cn1,k

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

Research output: Contribution to journalArticlepeer-review

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 Gn1,k constructed from the circulant graph Cn1,k by subdividing its edges. We have shown that, for k=2, Gn1,k has an unbounded metric dimension, and for k=3 and 4, Gn1,k has a bounded metric dimension.

Original languageEnglish
Article number4197678
JournalDiscrete Dynamics in Nature and Society
Volume2020
DOIs
Publication statusPublished - 2020

ASJC Scopus subject areas

  • Modelling and Simulation

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