Power graphs: A survey
Jemal H. Abawajy,Andrei V. Kelarev,Morshed U. Chowdhury +2 more
- Vol. 1, Iss: 2, pp 125-147
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.read more
Citations
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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.
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Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups
Asma Hamzeh,Ali Ashrafi Reza +1 more
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.
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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.
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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.
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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
Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
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
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.