Abstract:The enhanced power graph of a finite group is the graph whose vertex set is the set of the elements of this group, and two distinct vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split graphs and threshold graphs. 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 C… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.