Resolvability in Subdivision of Circulant Networks Cn1,k
Joint Authors
Abbas, Ghulam
Imran, Muhammad
Wei, Jianxin
Bokhary, Syed Ahtsham Ul Haq
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Wei, Jianxin& Bokhary, Syed Ahtsham Ul Haq& Abbas, Ghulam& Imran, Muhammad. 2020. Resolvability in Subdivision of Circulant Networks Cn1,k. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1153036
Modern Language Association (MLA)
Wei, Jianxin…[et al.]. Resolvability in Subdivision of Circulant Networks Cn1,k. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1153036
American Medical Association (AMA)
Wei, Jianxin& Bokhary, Syed Ahtsham Ul Haq& Abbas, Ghulam& Imran, Muhammad. Resolvability in Subdivision of Circulant Networks Cn1,k. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1153036
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153036