Eccentric Harmonic Index for the Cartesian Product of Graphs
Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2/ea+eb for the edges vavb, where ea is the eccentricity of the ath vertex of the graph ρ. We symbolize the eccentric harmonic index (EHI) as He=Heρ. In this article, we determine He for the Cartesian p...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9219613 |
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| author | Kamel Jebreen Muhammad Haroon Aftab M. I. Sowaity B. Sharada A. M. Naji M. Pavithra |
| author_facet | Kamel Jebreen Muhammad Haroon Aftab M. I. Sowaity B. Sharada A. M. Naji M. Pavithra |
| author_sort | Kamel Jebreen |
| collection | DOAJ |
| description | Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2/ea+eb for the edges vavb, where ea is the eccentricity of the ath vertex of the graph ρ. We symbolize the eccentric harmonic index (EHI) as He=Heρ. In this article, we determine He for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for He of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry. |
| format | Article |
| id | doaj-art-7c21b886da2f4538aaae91700d52ee01 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7c21b886da2f4538aaae91700d52ee012025-02-03T05:57:59ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9219613Eccentric Harmonic Index for the Cartesian Product of GraphsKamel Jebreen0Muhammad Haroon Aftab1M. I. Sowaity2B. Sharada3A. M. Naji4M. Pavithra5Department of MathematicsDepartment of Mathematics and StatisticsDepartment of MathematicsDepartment of Studies in Computer ScienceDepartment of MathematicsDepartment of Studies in MathematicsSuppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2/ea+eb for the edges vavb, where ea is the eccentricity of the ath vertex of the graph ρ. We symbolize the eccentric harmonic index (EHI) as He=Heρ. In this article, we determine He for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for He of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry.http://dx.doi.org/10.1155/2022/9219613 |
| spellingShingle | Kamel Jebreen Muhammad Haroon Aftab M. I. Sowaity B. Sharada A. M. Naji M. Pavithra Eccentric Harmonic Index for the Cartesian Product of Graphs Journal of Mathematics |
| title | Eccentric Harmonic Index for the Cartesian Product of Graphs |
| title_full | Eccentric Harmonic Index for the Cartesian Product of Graphs |
| title_fullStr | Eccentric Harmonic Index for the Cartesian Product of Graphs |
| title_full_unstemmed | Eccentric Harmonic Index for the Cartesian Product of Graphs |
| title_short | Eccentric Harmonic Index for the Cartesian Product of Graphs |
| title_sort | eccentric harmonic index for the cartesian product of graphs |
| url | http://dx.doi.org/10.1155/2022/9219613 |
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