On the third ABC index of trees and unicyclic graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912277755592704 |
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| author | Song, Rui |
| author_facet | Song, Rui |
| contents | Let $G=(V,E)$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. The third atom-bond connectivity index, $ABC_3$ index, of $G$ is defined as $ABC_3(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e(u)+e(v)-2}{e(u)e(v)}}$, where eccentricity $e(u)$ is the largest distance between $u$ and any other vertex of $G$, namely $e(u)=\max\{d(u,v)|v\in V(G)\}$. This work determines the maximal $ABC_3$ index of unicyclic graphs with any given girth and trees with any given diameter, and characterizes the corresponding graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the third ABC index of trees and unicyclic graphs Song, Rui Combinatorics Let $G=(V,E)$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. The third atom-bond connectivity index, $ABC_3$ index, of $G$ is defined as $ABC_3(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e(u)+e(v)-2}{e(u)e(v)}}$, where eccentricity $e(u)$ is the largest distance between $u$ and any other vertex of $G$, namely $e(u)=\max\{d(u,v)|v\in V(G)\}$. This work determines the maximal $ABC_3$ index of unicyclic graphs with any given girth and trees with any given diameter, and characterizes the corresponding graphs. |
| title | On the third ABC index of trees and unicyclic graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2309.02036 |