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- W4289597933 abstract "The power graph $P(G)$ of a group $G$ is a simple graph with the vertex set $G$ such that two distinct vertices $u,v in G$ are adjacent in $P(G)$ if and only if $u^m = v$ or $v^m = u$, for some $m in mathbb{N}$. The purpose of this paper is to introduce the notion of a power graph for gyrogroups. Using this, we investigate the combinatorial properties of a certain gyrogroup, say $G(n)$, of order $2^n$ for $n geq 3$. In particular, we determine the Hamiltonicity and planarity of the power graph of $G(n)$. Consequently, we calculate distant properties, resolving polynomial, Hosoya and reciprocal Hosoya polynomials, characteristic polynomials, and the spectral radius of the power graph of $G(n)$." @default.
- W4289597933 created "2022-08-03" @default.
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- W4289597933 date "2022-08-01" @default.
- W4289597933 modified "2023-10-16" @default.
- W4289597933 title "On the power graph of a certain gyrogroup" @default.
- W4289597933 doi "https://doi.org/10.48550/arxiv.2208.00743" @default.
- W4289597933 hasPublicationYear "2022" @default.
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