Hosoya properties of power graphs over certain groups

2022/12/23 by Singh, Yogendra, Tiwari, Anand Kumar, Ali, Fawad
#05C07 #05C50 #15A27 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.12459

Abstract

The power graph denoted by P(G) of a finite group G is a graph with vertex set G and there is an edge between two distinct elements u, v ∈ G if and only if u^m = v or v^m = u for some m ∈ 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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