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Open AccessJournal ArticleDOI

Power graphs: A survey

TLDR
This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature.
Abstract
This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.

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Citations
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Journal ArticleDOI

A study of enhanced power graphs of finite groups

TL;DR: In this paper, the enhanced power graph is defined as the graph with vertex set G such that two vertices x and y are adjacent if they are contained in the same cyclic subgroup.
Journal ArticleDOI

Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups

TL;DR: In this paper, the characteristic polynomial of the power graph for dihedral, semi-dihedral, cyclic and dicyclic groups was computed and the spectrum and Laplacian spectrum of these graphs were computed.
Journal ArticleDOI

The Rainbow Connection Number of the Power Graph of a Finite Group

TL;DR: The rainbow connection numbers of power graphs of some nonnilpotent groups are given and it is shown that the rainbow connection number of Gamma G is at most three if G has no maximal involutions.
Journal ArticleDOI

Power graphs of (non)orientable genus two

TL;DR: In this paper, the power graph of a finite group is defined as the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other.
Journal ArticleDOI

On the enhanced power graph of a finite group

TL;DR: In this article, the minimum degree, indescrete power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup.
References
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Book

Graph theory

Frank Harary
Book

Algebraic Graph Theory

TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Journal ArticleDOI

The MAGMA algebra system I: the user language

TL;DR: MAGMA as mentioned in this paper is a new system for computational algebra, and the MAGMA language can be used to construct constructors for structures, maps, and sets, as well as sets themselves.
Book

A Course in the Theory of Groups

TL;DR: A detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative is given in this article, where the reader is provided with only a basic knowledge of modern algebra.
Book

Fundamentals of semigroup theory

John Howie
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.