On Harmonic Index and Diameter of Quasi-Tree Graphs
The harmonic index of a graph G (HG) is defined as the sum of the weights 2/du+dv for all edges uv of G, where du is the degree of a vertex u in G. In this paper, we show that HG≥DG+5/3−n/2 and HG≥1/2+2/3n−2DG, where G is a quasi-tree graph of order n and diameter DG. Indeed, we show that both lower...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6650407 |
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| author | A. Abdolghafourian Mohammad A. Iranmanesh |
| author_facet | A. Abdolghafourian Mohammad A. Iranmanesh |
| author_sort | A. Abdolghafourian |
| collection | DOAJ |
| description | The harmonic index of a graph G (HG) is defined as the sum of the weights 2/du+dv for all edges uv of G, where du is the degree of a vertex u in G. In this paper, we show that HG≥DG+5/3−n/2 and HG≥1/2+2/3n−2DG, where G is a quasi-tree graph of order n and diameter DG. Indeed, we show that both lower bounds are tight and identify all quasi-tree graphs reaching these two lower bounds. |
| format | Article |
| id | doaj-art-6aa59e568df842fe9a63ed9622397837 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6aa59e568df842fe9a63ed96223978372025-02-03T05:52:38ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66504076650407On Harmonic Index and Diameter of Quasi-Tree GraphsA. Abdolghafourian0Mohammad A. Iranmanesh1Department of Mathematics, Yazd University, 89195-741 Yazd, IranDepartment of Mathematics, Yazd University, 89195-741 Yazd, IranThe harmonic index of a graph G (HG) is defined as the sum of the weights 2/du+dv for all edges uv of G, where du is the degree of a vertex u in G. In this paper, we show that HG≥DG+5/3−n/2 and HG≥1/2+2/3n−2DG, where G is a quasi-tree graph of order n and diameter DG. Indeed, we show that both lower bounds are tight and identify all quasi-tree graphs reaching these two lower bounds.http://dx.doi.org/10.1155/2021/6650407 |
| spellingShingle | A. Abdolghafourian Mohammad A. Iranmanesh On Harmonic Index and Diameter of Quasi-Tree Graphs Journal of Mathematics |
| title | On Harmonic Index and Diameter of Quasi-Tree Graphs |
| title_full | On Harmonic Index and Diameter of Quasi-Tree Graphs |
| title_fullStr | On Harmonic Index and Diameter of Quasi-Tree Graphs |
| title_full_unstemmed | On Harmonic Index and Diameter of Quasi-Tree Graphs |
| title_short | On Harmonic Index and Diameter of Quasi-Tree Graphs |
| title_sort | on harmonic index and diameter of quasi tree graphs |
| url | http://dx.doi.org/10.1155/2021/6650407 |
| work_keys_str_mv | AT aabdolghafourian onharmonicindexanddiameterofquasitreegraphs AT mohammadairanmanesh onharmonicindexanddiameterofquasitreegraphs |