论文标题
有限阿贝尔组和二面体组的联合订单图
Co-Prime Order graph of a finite abelian Group and Dihedral Group
论文作者
论文摘要
给定有限组的\ textbf {co-Prime订单graph} $θ（g）$是一个简单的无向图，其顶点集是$ g $本身，而如果$ gcd（o（x），o（x），o（y（y（y）），$θ（g）$ in $θ（g）$ in $θ（g）中的任何两个顶点x，y都是相邻的。在本文中，我们找到了一个精确的公式，可以计算有限的Abelian组或二面体组的共同顺序图中的顶点$ d_n $。 {\ Mathbb {z} _q}^s $或二面体组$ d_ {p^n} $。 关键词和短语：联合秩序图，有限的Abelian组，二面部组，Laplacian Spectrum。
The \textbf{Co-Prime Order Graph} $Θ(G)$ of a given finite group is a simple undirected graph whose vertex set is the group $G$ itself, and any two vertexes x,y in $Θ(G)$ are adjacent if and only if $gcd(o(x),o(y))=1$ or prime. In this paper, we find a precise formula to count the degree of a vertex in the Co-Prime Order graph of a finite abelian group or Dihedral group $D_n$.We also investigate the Laplacian spectrum of the Co-Prime Order Graph $Θ(G)$ when G is finite abelian p-group, ${\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s$ or Dihedral group $D_{p^n}$. Key Words and Phrases: Co-Prime Order graph,finite abelian group,Dihedral group, Laplacian spectrum.
