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

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The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a,b∈S are adjacent if and only if a≠b and am=b or bm=a for some positive integer m. In
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‎This paper concerns aspects of various graphs whose vertex set is a group \$G\$‎ ‎and whose edges reflect group structure in some way (so that‎, ‎in particular‎, ‎they are invariant under the action
Abstract The directed power graph of a group G is the digraph with vertex set G, having an arc from y to x whenever x is a power of y; the undirected power graph has an edge joining x and y whenever
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The punctured power graph P (G) of a finite group G is the graph which has as vertex set the nonidentity elements of G, where two distinct elements are adjacent if one is a power of the other. We
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The powergraph is always perfect; and the groups whose power graph is a threshold graph are determined completely.
Introduction. The purpose of this paper is to clarify the structure of finite groups satisfying the following condition: (CN): the centralizer of any nonidentity element is nilpotent. Throughout this
THE class u(u> 3) of a doubly transitive group of degree n is, according to Bochert,f greater than \n — § Vw. If we confine our attention however to those doubly transitive groups in which one of the