Some results on the non-commuting graph of a finite group

被引：0

作者：

Moradipour, K. ^{[1
]}

Ilangovan, Sh ^{[2
]}

Rashid, S. ^{[3
]}

机构：

[1] Tech & Vocat Univ, Lorestan Branch, Fac Khorramabad, Dept Math, Lorestan, Iran

[2] Univ Nottingham Malaysia, Campus Jalan Broga, Semenyih 43500, Selangor Darul, Malaysia

[3] Islamic Azad Univ, Yadegar E Imam Khomeini RAH Branch, Coll Basic Sci, Dept Math, Tehran, Iran

来源：

SCIENCEASIA | 2019年 / 45卷 / 05期

关键词：

Non-commuting graph; metacyclic p-group; isoclinic; PROBABILITY;

D O I：

10.2306/scienceasia1513-1874.2019.45.482

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Let G be a metacyclic p-group, and let Z(G) be its center. The non-commuting graph Gamma(G) of a metacyclic p-group G is defined as the graph whose vertex set is G-Z(G), and two distinct vertices x and y are connected by an edge if and only if the commutator of x and y is not the identity. In this paper, we give some graph theoretical properties of the non-commuting graph Gamma(G) . Particularly, we investigate planarity, completeness, clique number and chromatic number of such graph. Also, we prove that if G(1) and G(2) are isoclinic metacyclic p-groups, then their associated graphs are isomorphic.

引用

页码：482 / 487

页数：6

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