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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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 finite groups whose power graph is a cograph
TL;DR: In this article, it was shown that the power graph of a P 4 -free graph is called a cograph, and that all groups whose power graphs are cographs can be characterized by a condition only involving elements whose orders are prime or the product of two (possibly equal) primes.
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On the minimum degree of the power graph of a finite cyclic group
Ramesh Prasad Panda,Ramesh Prasad Panda,Kamal Lochan Patra,Kamal Lochan Patra,Binod Kumar Sahoo,Binod Kumar Sahoo +5 more
TL;DR: In this article, it was shown that for any integer n ≥ 3, under certain conditions involving the prime divisors of the cyclic group of order n, one can identify at most n-1 vertices such that the degree of at least one of these vertices is equal to that of the prime degree of the other vertices.
Journal ArticleDOI
Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications
TL;DR: It is proved that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight.
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Notes on the Co-prime Order Graph of a Group
TL;DR: In this paper , the vertex-connectivity of the co-prime order graphs of a cyclic group, a dihedral group and a generalized quaternion group was studied.
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.