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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The co-prime order graph associated with a finite group
Xuanlong Ma,Zhonghua Wang +1 more
TL;DR: In this paper, the authors characterized all finite groups whose co-prime order graphs are complete and classified all the finite groups that have planar planar co-order graphs, including cyclic groups, dihedral groups and generalized quaternion groups.
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On the order supergraph of the power graph of a finite group
Xuanlong Ma,Huadong Su +1 more
TL;DR: In this paper, the independence number of the order supergraph of a finite group G is studied and a question was posed by Hamzeh and Ashrafi, and the answer was given.
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On some characterizations of strong power graphs of finite groups
A. K. Bhuniya,Sudip Bera +1 more
TL;DR: In this paper, the Spectrum and permanent of the Laplacian matrix of the strong power graph of the Caley graph were found for any finite group of order n, where n is the number of vertices in the graph.
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On Sum of Powers of the Laplacian Eigenvalues of Power Graphs of Certain Finite Groups
TL;DR: Borders for Laplacian-energy-like (LEL) invariant of the same graphs are obtained by concentrating on sum of powers of the non-zero LaPLacian eigenvalues of G ( Z n ) and G ( D n ) .
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Intersection graphs of general linear groups
Mai Hoang Bien,Do Hoang Viet +1 more
TL;DR: In this article, the intersection graph Γ(GLn(F)) of a general linear group of degree n > 1 over a field is a simple undirected graph whose vertex set includes all nontrivial proper graphs.
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.
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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.