The diameter of the commuting graph of a finite group with trivial centre
G. L. Morgan, C. W. Parker
TL;DR
This paper investigates the structure of the commuting graph of finite groups with trivial center, establishing that its connected components have a maximum diameter of 10.
Contribution
It proves an upper bound of 10 on the diameter of connected components in the commuting graph of such groups, advancing understanding of their algebraic structure.
Findings
Connected components have diameter at most 10
Provides bounds on the structure of commuting graphs
Enhances understanding of finite groups with trivial center
Abstract
The commuting graph of a finite group with trivial centre is examined. It is shown that the connected components of the commuting graph have diameter at most 10.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems