# On finite groups whose power graph is a cograph

```@article{Cameron2021OnFG,
title={On finite groups whose power graph is a cograph},
author={Peter J. Cameron and Pallabi Manna and Ranjit Mehatari},
journal={Journal of Algebra},
year={2021}
}```
• Published 27 June 2021
• Mathematics
• Journal of Algebra
• Mathematics
• 2021
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.
• Mathematics
• 2021
We determine the diameter of every connected component of the complement of the power graph of a finite group, which completely answers a question by Peter J. Cameron.
• Mathematics
• 2022
We prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classiﬁed by Manna, Cameron and Mehatari [The Electronic Journal of
• Mathematics
Journal of Group Theory
• 2023
Abstract In recent work, Cameron, Manna and Mehatari have studied the finite groups whose power graph is a cograph, which we refer to as power-cograph groups. They classify the nilpotent groups with
• Mathematics
• 2022
A graph is called chordal if it forbids induced cycles of length 4 or more. In this paper, we investigate chordalness of power graph of ﬁnite groups. In this direction we characterize direct product
• Mathematics
• 2023
For a ﬁnite group G the co-prime graph Γ( G ) is deﬁned as a graph with vertex set G in which two distinct vertices x and y are adjacent if and only if gcd ( o ( x ) , o ( y )) = 1 where o ( x ) and
• Mathematics
• 2022
We say that a finite group G satisfies the independence property if, for every pair of distinct elements x and y of G, either {x, y} is contained in a minimal generating set for G, or one of x and y
• Mathematics
• 2022
. The diﬀerence graph D ( G ) of a ﬁnite group G is the diﬀerence of enhanced power graph of G and power graph of G , with all isolated vertices are removed. In this paper we study the connectedness