论文标题
在某个陀螺仪的功率图上
On the power graph of a certain gyrogroup
论文作者
论文摘要
一个组$ g $的电源图$ p（g）$是一个简单的图形，带顶点套装$ g $，使得两个不同的vertices $ u，in g $ in g $ in $ p（g）$ in $ p（g）$，并且仅当$ m = v $或$ v $或$ v^m = u $，对于某些$ m \ in \ nr \ mathbb {n} $。本文的目的是介绍陀螺仪的幂图的概念。使用此过程，我们调查了某个gyrogroup的组合属性，例如$ g（n）$，$ n \ geq 3 $的订单$ 2^n $。特别是，我们确定了$ g（n）$的功率图的汉密尔顿性和平面度。因此，我们计算遥远的特性，解决多项式，霍索亚和相互的霍索亚多项式，特征多项式以及$ g（n）$的功率图的光谱半径。
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 $G(n)$.
