Some properties of various graphs associated with finite groups
Group Theory
2018-06-07 v1
Abstract
In this paper we have investigated some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it has been shown that the simple group can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we have obtained an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.
Cite
@article{arxiv.1806.02102,
title = {Some properties of various graphs associated with finite groups},
author = {Xiaoyou Chen and Alireza Moghaddamfar and Mahsa Zohourattar},
journal= {arXiv preprint arXiv:1806.02102},
year = {2018}
}
Comments
13 pages