Co-prime order graphs of finite Abelian groups and dihedral groups

被引：8

作者：

Sehgal, Amit ^{[1
]}

Manjeet ^{[1
]}

Singh, Dalip ^{[2
]}

机构：

[1] Pt NRS Govt Coll, Dept Math, Rohtak, Haryana, India

[2] Maharshi Dayanand Univ, Dept Math, Rohtak, Haryana, India

来源：

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS | 2021年 / 23卷 / 03期

关键词：

Co-prime order graph; finite Abelian group; dihedral group; Laplacian spectrum; POWER GRAPHS;

D O I：

10.22436/jmcs.023.03.03

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The co-prime order graph Theta(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 Theta(G) are adjacent if and only if gcd(o(x), o(y)) = 1 or prime. In this paper, we derive a precise formula to count the vertex's degree in the co-prime order graph of a finite Abelian group or dihedral group.We also investigate the Laplacian spectrum of the co-prime order graph Theta(G) when G is a finite Abelian p-group, Z(p)(t) x Z(q)(s )or a dihedral group D-p(n).

引用

页码：196 / 202

页数：7

共 11 条

[1] Power Graphs: A Survey [J].