On the Maximum Atom-Bond Sum-Connectivity Index of Graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916136377909248 |
|---|---|
| author | Alraqad, Tariq Saber, Hisham Ali, Akbar Albalahi, Abeer M. |
| author_facet | Alraqad, Tariq Saber, Hisham Ali, Akbar Albalahi, Abeer M. |
| contents | The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over $1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In this paper, we study the maximum values of the ABS index over graphs with given parameters. More specifically, we determine the maximum ABS index of connected graphs of a given order and with a fixed (i) minimum degree, (ii) maximum degree, (iii) chromatic number, (iv) independence number, or (v) number of pendent vertices. We also characterize the graphs attaining the maximum ABS values in all of these classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Maximum Atom-Bond Sum-Connectivity Index of Graphs Alraqad, Tariq Saber, Hisham Ali, Akbar Albalahi, Abeer M. General Mathematics 05C07, 05C09, 05C35 The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over $1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In this paper, we study the maximum values of the ABS index over graphs with given parameters. More specifically, we determine the maximum ABS index of connected graphs of a given order and with a fixed (i) minimum degree, (ii) maximum degree, (iii) chromatic number, (iv) independence number, or (v) number of pendent vertices. We also characterize the graphs attaining the maximum ABS values in all of these classes. |
| title | On the Maximum Atom-Bond Sum-Connectivity Index of Graphs |
| topic | General Mathematics 05C07, 05C09, 05C35 |
| url | https://arxiv.org/abs/2302.01905 |