Resolvability in Subdivision of Circulant Networks Cn1,k
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/4197678 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850227815110148096 |
|---|---|
| author | Jianxin Wei Syed Ahtsham Ul Haq Bokhary Ghulam Abbas Muhammad Imran |
| author_facet | Jianxin Wei Syed Ahtsham Ul Haq Bokhary Ghulam Abbas Muhammad Imran |
| author_sort | Jianxin Wei |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-24e7ad24b97e462b9373c9204898d866 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-24e7ad24b97e462b9373c9204898d8662025-08-20T02:04:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/41976784197678Resolvability in Subdivision of Circulant Networks Cn1,kJianxin Wei0Syed Ahtsham Ul Haq Bokhary1Ghulam Abbas2Muhammad Imran3School of Mathematics and Statistics Science, Ludong University, Yantai 264025, Shandong, ChinaCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAECirculant 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.http://dx.doi.org/10.1155/2020/4197678 |
| spellingShingle | Jianxin Wei Syed Ahtsham Ul Haq Bokhary Ghulam Abbas Muhammad Imran Resolvability in Subdivision of Circulant Networks Cn1,k Discrete Dynamics in Nature and Society |
| title | Resolvability in Subdivision of Circulant Networks Cn1,k |
| title_full | Resolvability in Subdivision of Circulant Networks Cn1,k |
| title_fullStr | Resolvability in Subdivision of Circulant Networks Cn1,k |
| title_full_unstemmed | Resolvability in Subdivision of Circulant Networks Cn1,k |
| title_short | Resolvability in Subdivision of Circulant Networks Cn1,k |
| title_sort | resolvability in subdivision of circulant networks cn1 k |
| url | http://dx.doi.org/10.1155/2020/4197678 |
| work_keys_str_mv | AT jianxinwei resolvabilityinsubdivisionofcirculantnetworkscn1k AT syedahtshamulhaqbokhary resolvabilityinsubdivisionofcirculantnetworkscn1k AT ghulamabbas resolvabilityinsubdivisionofcirculantnetworkscn1k AT muhammadimran resolvabilityinsubdivisionofcirculantnetworkscn1k |