## 10 Citations

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

- 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.

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

- 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.

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

- 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…

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

- Mathematics
- 2022

Cameron, Manna and Mehatari investigated the question of which ﬁnite groups admit a power graph that is a cograph, also called power-cograph groups (Journal of Algebra 591 (2022)). They give a…

### On chordalness of power graphs of finite groups

- 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…

### Finite groups satisfying the independence property

- 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…

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

- 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…

## References

SHOWING 1-10 OF 43 REFERENCES

### The power graph of a torsion-free group

- Mathematics
- 2017

The power graphP(G) of a group G is the graph whose vertex set is G, with x and y joined if one is a power of the other; the directed power graph$$\overrightarrow{P}(G)$$P→(G) has the same vertex…

### Undirected power graphs of semigroups

- Mathematics
- 2009

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…

### On the Connectivity and Independence Number of Power Graphs of Groups

- MathematicsGraphs Comb.
- 2020

All groups whose power graphs have finite independence number are characterized, and it is shown that they have clique cover number equal to their independence number, and this number is calculated.

### On the Structure of the Power Graph and the Enhanced Power Graph of a Group

- MathematicsElectron. J. Comb.
- 2017

It is proved that for every group G, the clique number of the power graph of $G$ is at most countably infinite and the graph is called theenhanced power graph.

### Graphs defined on groups

- Mathematics
- 2021

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…

### The power graph of a finite group, II

- Mathematics
- 2010

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…

### On the punctured power graph of a finite group

- MathematicsAustralas. J Comb.
- 2015

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…

### Forbidden Subgraphs of Power Graphs

- MathematicsElectron. J. Comb.
- 2021

The powergraph is always perfect; and the groups whose power graph is a threshold graph are determined completely.

### Finite groups with nilpotent centralizers

- Mathematics
- 1961

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…

### On a class of doubly transitive groups

- Mathematics
- 1972

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…