The Szeged Index of Power Graph of Finite Groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912676609785856 |
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| author | Banerjee, Subarsha |
| author_facet | Banerjee, Subarsha |
| contents | The Szeged index of a graph is an invariant with several applications in chemistry. The power graph of a finite group $G$ is a graph having vertex set as $G$ in which two vertices $u$ and $v$ are adjacent if $v=u^m$ or $u=v^n$ for some $m,n\in \mathbb{N}$. In this paper, we first obtain a formula for the Szeged index of the generalized join of graphs. As an application, we obtain the Szeged index of the power graph of the finite cyclic group $\mathbb Z_n$ for any $n>2$. We further obtain a relation between the Szeged index of the power graph of $\mathbb Z_n$ and the Szeged index of the power graph of the dihedral group $\mathrm{D}_n$. We also provide SAGE codes for evaluating the Szeged index of the power graph of $\mathbb{Z}_n$ and $\mathrm{D}_n$ at the end of this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Szeged Index of Power Graph of Finite Groups Banerjee, Subarsha Combinatorics 05C09, 05C25 The Szeged index of a graph is an invariant with several applications in chemistry. The power graph of a finite group $G$ is a graph having vertex set as $G$ in which two vertices $u$ and $v$ are adjacent if $v=u^m$ or $u=v^n$ for some $m,n\in \mathbb{N}$. In this paper, we first obtain a formula for the Szeged index of the generalized join of graphs. As an application, we obtain the Szeged index of the power graph of the finite cyclic group $\mathbb Z_n$ for any $n>2$. We further obtain a relation between the Szeged index of the power graph of $\mathbb Z_n$ and the Szeged index of the power graph of the dihedral group $\mathrm{D}_n$. We also provide SAGE codes for evaluating the Szeged index of the power graph of $\mathbb{Z}_n$ and $\mathrm{D}_n$ at the end of this paper. |
| title | The Szeged Index of Power Graph of Finite Groups |
| topic | Combinatorics 05C09, 05C25 |
| url | https://arxiv.org/abs/2510.25686 |