Power Graph Classes and Overfullness

2025/08/02 by Feinsilber, Elie
#05C15 (Secondary) #05C25 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.01417

Abstract

In this paper, we investigate the edge-coloring number of the power graph of a finite group. We characterize which finite groups have overfull power graphs, showing that this occurs if and only if the group is cyclic of odd prime power order. We then show that this classsifies the class of power graphs: The power graph of a finite group is Class 2 if and only if the group is cyclic of odd prime power order.

Citations

• Group nilpotency from a graph point of view
• Graphs defined on groups
• The NP-Completeness of Edge-Coloring

Related

• Power Graphs of Finite Group
• Power Graphs of Finite Groups
• A combinatorial characterization of finite groups of prime exponent
• On neighborhoods in the enhanced power graph associated with a finite group
• Some results in a new power graphs in finite groups