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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Normal subgroup based power graph of finite groups
TL;DR: In this paper, the authors characterized all pairs (G, N) of a finite group G and a proper non-trivial normal subgroup N of G such that G is a split, bisplit and n-1)-decrease bisplits.
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On the minimum cut-sets of the power graph of a finite cyclic group
TL;DR: In this paper , the minimum cut-sets of the power graph of a finite group of order (G) were characterized in terms of the number of distinct prime divisors of G. For an integer n ≥ 2, the cut-set of G = 0.
Power Graphs of Finite Groups
TL;DR: In this paper , the authors give lower bounds for the maximum length of a cycle in the power graph of a group and the quotient of the power graphs under some equivalence relations.
On the super graphs and reduced super graphs of some finite groups
TL;DR: In this article , the authors characterized the dominant vertices for the order super commuting graph ∆ o (G ) of G and proved that for n ≥ 4 the identity element is the only dominant vertex of ∆ O ( S n ) and ∆O( A n ).
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On the power graph of the direct product of two groups
TL;DR: In this paper, it was shown that the power graph of a finite group P(G) is not isomorphic to either of the direct, cartesian and normal product of their power 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.
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.
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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.