Notes on the diameter of the complement of the power graph of a finite group
Xuanlong Ma, Alireza Doostabadi, Kaishun Wang
TL;DR
This paper calculates the diameter of the complement of the power and enhanced power graphs for finite groups, providing complete answers to previously open questions in group theory graph analysis.
Contribution
It precisely determines the diameters of these graph complements for all finite groups, resolving two open questions posed by Peter J. Cameron.
Findings
Diameters of the complement of the power graph are fully characterized.
Diameters of the complement of the enhanced power graph are fully characterized.
The results answer two open questions in the study of group-related graphs.
Abstract
We determine the diameter of every connected component of the complement of the power graph and the enhanced power graph of a finite group, which completely answers two questions by Peter J. Cameron.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Graph Theory Research · Graph theory and applications