Power graphs: A survey
Jemal H. Abawajy,Andrei V. Kelarev,Morshed U. Chowdhury +2 more
- Vol. 1, Iss: 2, pp 125-147
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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
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Perfect codes in proper reduced power graphs of finite groups
TL;DR: In this article, a graph with vertex set V(Γ) is a graph and a subset T of V(T) is an independent set such that every vertex in T is adjacent to exactly one vertex in C.
Journal ArticleDOI
A survey on enhanced power graphs of finite groups
TL;DR: In this paper , the authors survey known results on enhanced power graphs of finite groups and open problems, questions and suggestions for future work are also included, as well as some open problems.
Posted Content
Some results on the reduced power graph of a group
R. Rajkumar,T. Anitha +1 more
TL;DR: In this article, the authors classify finite groups whose reduced power graph is one of complete k-partite, acyclic, triangle free or claw-free (resp. complete k)-partite and triangle free).
Journal ArticleDOI
The Complexity of Power Graphs Associated With Finite Groups
TL;DR: In this paper, the complexity of clique-replaced graphs is studied and some explicit formulas concerning the complexity for various groups G such as the cyclic group of order n, the simple groups L_2(q), the extra-special p-groups of order p^3, the Frobenius groups, etc.
Journal ArticleDOI
A group sum inequality and its application to power graphs
TL;DR: In this paper, it was shown that among all finite groups of a given order, the cyclic group of that order has the maximum number of undirected edges in its directed power graph.
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.
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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.