4 papers · 1 filter
Generalizing the enhanced power graph of a group with respect to automorphisms
Abbas Mohammadian, Ismail Guloglu, Ahmad Erfanian +1
We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the en…
Triangle-free cyclic conjugacy class graph of a finite group
Mark L. Lewis, Abbas Mohammadian
We generalize the enhanced power graph by replacing elements with conjugacy classes. The main result of this paper is to determine when this graph is triangle-free.
Neighborhoods, connectivity, and diameter of the nilpotent graph of a finite group
Costantino Delizia, Michele Gaeta, Mark L. Lewis +1
The nilpotent graph of a group is the simple and undirected graph whose vertices are the elements of and two distinct vertices are adjacent if they generate a nilpotent sub…
On neighborhoods in the enhanced power graph associated with a finite group
Mark L. Lewis, Carmine Monetta
This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite -…