2021/04/10 by Xuanlong Ma, Ma, Xuanlong, Yubo Lv +4 · 1 citation
Computer Science · Engineering · Mathematics · #05C25 #05C38 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2104.04754
openalex publication_date 2021/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal graphs and cographs. These results partly answer a question posed by Peter J. Cameron.