Resolvability in subdivision of circulant networks \(C_n[1, k]\)
type: Item
instance of: scholarly article
title: Resolvability in subdivision of circulant networks \(C_n[1, k]\)
zbMATH Open document ID: 1459.05069
DOI: 10.1155/2020/4197678
author: Jianxin Wei
author: Ghulam Abbas
author: M. Imran
author: Syed Ahtsham Ul Haq Bokhary
published in: Discrete Dynamics in Nature and Society
publication date: 2020-10-14T00:00:00Z
review text: Summary: 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 \(G_n[1, k]\) constructed from the circulant graph \(C_n[1, k]\) by subdividing its edges. We have shown that, for \(k=2\), \(G_n[1, k]\) has an unbounded metric dimension, and for \(k=3\) and 4, \(G_n[1, k]\) has a bounded metric dimension.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 7260910
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4197678
OpenAlex ID: W3088316435
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description: scientific article; zbMATH DE number 7260910