Distance Measurements Related to Cartesian Product of Cycles
Graph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the literature. An important discussion is based on distance between tw...
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| Main Authors: | , , , , , |
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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/10.1155/2020/6371694 |
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| _version_ | 1849411036594044928 |
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| author | Xiaoli Qiang Saima Nazeer Yu-Ming Chu Muhammad Awais Umar Imrana Kousar Ammara Sehar |
| author_facet | Xiaoli Qiang Saima Nazeer Yu-Ming Chu Muhammad Awais Umar Imrana Kousar Ammara Sehar |
| author_sort | Xiaoli Qiang |
| collection | DOAJ |
| description | Graph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the literature. An important discussion is based on distance between two nodes in a network which may include closeness of objects, centrality of objects, average path length between objects, and vertex eccentricity. For example, (1) disease transmission networks: closeness and centrality of objects are used to measure vulnerability to particular disease and its infectivity; (2) routing networks: eccentricity of objects is used to find vertices which form the periphery objects of the network. In this manuscript, we have discussed distance measurements including center, periphery, and average eccentricity for the Cartesian product of two cycles. The results are obtained using the definitions of eccentricity, radius, and diameter of a graph, and all possible cases (for different parity of length of cycles) have been proved. |
| format | Article |
| id | doaj-art-5ffc96826d2a4d45b6d3706756532aa1 |
| 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-5ffc96826d2a4d45b6d3706756532aa12025-08-20T03:34:53ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/63716946371694Distance Measurements Related to Cartesian Product of CyclesXiaoli Qiang0Saima Nazeer1Yu-Ming Chu2Muhammad Awais Umar3Imrana Kousar4Ammara Sehar5Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Mathematics, Lahore College For Women University, Lahore 54000, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaGovernment Degree College (B), Sharaqpur Sharif, Tehsil 39460, PakistanDepartment of Mathematics, Lahore College For Women University, Lahore 54000, PakistanDepartment of Mathematics, Lahore College For Women University, Lahore 54000, PakistanGraph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the literature. An important discussion is based on distance between two nodes in a network which may include closeness of objects, centrality of objects, average path length between objects, and vertex eccentricity. For example, (1) disease transmission networks: closeness and centrality of objects are used to measure vulnerability to particular disease and its infectivity; (2) routing networks: eccentricity of objects is used to find vertices which form the periphery objects of the network. In this manuscript, we have discussed distance measurements including center, periphery, and average eccentricity for the Cartesian product of two cycles. The results are obtained using the definitions of eccentricity, radius, and diameter of a graph, and all possible cases (for different parity of length of cycles) have been proved.http://dx.doi.org/10.1155/2020/6371694 |
| spellingShingle | Xiaoli Qiang Saima Nazeer Yu-Ming Chu Muhammad Awais Umar Imrana Kousar Ammara Sehar Distance Measurements Related to Cartesian Product of Cycles Journal of Mathematics |
| title | Distance Measurements Related to Cartesian Product of Cycles |
| title_full | Distance Measurements Related to Cartesian Product of Cycles |
| title_fullStr | Distance Measurements Related to Cartesian Product of Cycles |
| title_full_unstemmed | Distance Measurements Related to Cartesian Product of Cycles |
| title_short | Distance Measurements Related to Cartesian Product of Cycles |
| title_sort | distance measurements related to cartesian product of cycles |
| url | http://dx.doi.org/10.1155/2020/6371694 |
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