REALIZABILITY PROBLEM FOR COMMUTING GRAPHS

被引：2

作者：

Giudici, Michael ^{[1
]}

Kuzma, Bojan ^{[2
,3
]}

机构：

[1] Univ Western Australia, Ctr Math Symmetry & Computat, 35 Stirling Highway, Crawley, WA 6009, Australia

[2] Univ Primorska, Glagoljaska 8, SI-6000 Koper, Slovenia

[3] IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2016年 / 101卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

finite groups; finite semigroups; commuting graph; classification problem; DIAMETER;

D O I：

10.1017/S1446788716000148

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph of some semigroup. Moreover, we obtain complete classifications of the graphs with an isolated vertex or edge that are the commuting graph of a group and the cycles that are the commuting graph of a centrefree semigroup.

引用

页码：335 / 355

页数：21

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