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}
}
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11 Citations
Highly Influential Citations
2
Background Citations
7
Methods Citations
1
Results Citations
1

11 Citations

Notes on the diameter of the complement of the power graph of a finite group

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.

A note on the complement of the power graph of a finite group

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.

On groups with chordal power graph, including a classification in the case of finite simple groups

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…

Classification of non-solvable groups whose power graph is a cograph

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…

On chordalness of power graphs of finite groups

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…

Forbidden Subgraphs of co-prime Graphs of finite Groups

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…

Graphs on groups and their relations

Finite groups satisfying the independence property

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…

On Difference of Enhanced Power Graph and Power Graph of a Finite Group

. 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…

Generalisations of EPPO groups using graphs

References

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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…