Hosoya properties of power graphs over certain groups

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 d...

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Bibliographic Details
Published inarXiv.org
Main Authors Singh, Yogendra, Tiwari, Anand Kumar, Ali, Fawad
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.12.2022
Subjects
Graphs
Group theory
Polynomials
Vertex sets
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Summary: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 \(\Gamma\) is the total number of matchings in \(\Gamma\). 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.
ISSN:2331-8422