Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices
The first Zagreb eccentricity index E1℧ is the sum of square of eccentricities of the vertices, and the second Zagreb eccentricity index E2℧ is the sum of product squares of the eccentricities of the vertices. A linked graph G is called a cactus if any two of its cycles share only one vertex. In oth...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1677218 |
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| author | Ahmed Alamer Khalil Hadi Hakami Mohammad Rahim Rahimi Yasir Ahmad |
| author_facet | Ahmed Alamer Khalil Hadi Hakami Mohammad Rahim Rahimi Yasir Ahmad |
| author_sort | Ahmed Alamer |
| collection | DOAJ |
| description | The first Zagreb eccentricity index E1℧ is the sum of square of eccentricities of the vertices, and the second Zagreb eccentricity index E2℧ is the sum of product squares of the eccentricities of the vertices. A linked graph G is called a cactus if any two of its cycles share only one vertex. In other words, there are no two independent cycles that share an edge. Cactus graphs are also known as “block graphs” or “sensitized graphs.” They are closely related to chordal graphs and can be used to represent various types of networks, including communication networks and road networks. In this contribution, E1℧ and E2℧ values of cacti with k pendant vertices and k cycles, respectively, are considered. We determine the minimum E1,E2 indices for n order cacti with k pendant vertices and k cycles. |
| format | Article |
| id | doaj-art-be8b5573a3c94ca6989f83bc0b03b67c |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-be8b5573a3c94ca6989f83bc0b03b67c2025-02-03T07:23:47ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1677218Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity IndicesAhmed Alamer0Khalil Hadi Hakami1Mohammad Rahim Rahimi2Yasir Ahmad3Department of MathematicsDepartment of MathematicsDepartment of MathematicsCollege of Computer Science and Information TechnologyThe first Zagreb eccentricity index E1℧ is the sum of square of eccentricities of the vertices, and the second Zagreb eccentricity index E2℧ is the sum of product squares of the eccentricities of the vertices. A linked graph G is called a cactus if any two of its cycles share only one vertex. In other words, there are no two independent cycles that share an edge. Cactus graphs are also known as “block graphs” or “sensitized graphs.” They are closely related to chordal graphs and can be used to represent various types of networks, including communication networks and road networks. In this contribution, E1℧ and E2℧ values of cacti with k pendant vertices and k cycles, respectively, are considered. We determine the minimum E1,E2 indices for n order cacti with k pendant vertices and k cycles.http://dx.doi.org/10.1155/2024/1677218 |
| spellingShingle | Ahmed Alamer Khalil Hadi Hakami Mohammad Rahim Rahimi Yasir Ahmad Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices Journal of Mathematics |
| title | Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices |
| title_full | Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices |
| title_fullStr | Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices |
| title_full_unstemmed | Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices |
| title_short | Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices |
| title_sort | sharp lower bound of cacti graph with respect to zagreb eccentricity indices |
| url | http://dx.doi.org/10.1155/2024/1677218 |
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