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arXiv · 2212.12459

Hosoya properties of power graphs over certain groups

Yogendra Singh·Anand Kumar Tiwari·Fawad Ali
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Abstract

The power graph denoted by $\mathcal{P}(\mathcal{G})$ of a finite group $\mathcal{G}$ is a graph with vertex set $\mathcal{G}$ and there is an edge between two distinct elements $u, v \in \mathcal{G}$ if and only if $u^m = v$ or $v^m = u$ for some $m \in \mathbb{N}$. Depending on the distance, the Hosoya polynomial contains a lot of knowledge about graph invariants which can be used to determine well-known chemical descriptors. The Hosoya index of a graph $Γ$ is the total number of matchings in $Γ$. In this article, the Hosoya properties of the power graphs associated with a finite group, including the Hosoya index, Hosoya polynomial, and its reciprocal are calculated.

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Yogendra Singh, Anand Kumar Tiwari, Fawad Ali. 2022-12-23. Hosoya properties of power graphs over certain groups. https://arxiv.org/abs/2212.12459

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