Optimal Graphs in the Enhanced Mesh Networks
The degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so th...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/9869201 |
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| _version_ | 1832561467366309888 |
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| author | Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary |
| author_facet | Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary |
| author_sort | Muhammad Shahzad Akhtar |
| collection | DOAJ |
| description | The degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so the resulting graph may be thought of as being embedded in the complete graph. In a generality of the said problem, the graph is taken to be embedded in any connected host graph. In this article, host graph is considered as the enhanced mesh network constructed from the grid network. This article provides some exact values for the said problem and also gives some bounds for the optimal graphs. |
| format | Article |
| id | doaj-art-f34e59a09d5c4ef5b4f6ad99a5d5de56 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f34e59a09d5c4ef5b4f6ad99a5d5de562025-02-03T01:24:57ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/98692019869201Optimal Graphs in the Enhanced Mesh NetworksMuhammad Shahzad Akhtar0Muhammad Imran1Syed Ahtsham ul Haq Bokhary2Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaria University, Multan, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551 Al Ain, UAECenter for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaria University, Multan, PakistanThe degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so the resulting graph may be thought of as being embedded in the complete graph. In a generality of the said problem, the graph is taken to be embedded in any connected host graph. In this article, host graph is considered as the enhanced mesh network constructed from the grid network. This article provides some exact values for the said problem and also gives some bounds for the optimal graphs.http://dx.doi.org/10.1155/2020/9869201 |
| spellingShingle | Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary Optimal Graphs in the Enhanced Mesh Networks Journal of Mathematics |
| title | Optimal Graphs in the Enhanced Mesh Networks |
| title_full | Optimal Graphs in the Enhanced Mesh Networks |
| title_fullStr | Optimal Graphs in the Enhanced Mesh Networks |
| title_full_unstemmed | Optimal Graphs in the Enhanced Mesh Networks |
| title_short | Optimal Graphs in the Enhanced Mesh Networks |
| title_sort | optimal graphs in the enhanced mesh networks |
| url | http://dx.doi.org/10.1155/2020/9869201 |
| work_keys_str_mv | AT muhammadshahzadakhtar optimalgraphsintheenhancedmeshnetworks AT muhammadimran optimalgraphsintheenhancedmeshnetworks AT syedahtshamulhaqbokhary optimalgraphsintheenhancedmeshnetworks |