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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Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs
T. Anitha,R. Rajkumar +1 more
TL;DR: The reduced power graph as discussed by the authors is the graph whose vertex set is the set of all elements of G, and two vertices u and v are adjacent in ℛ𝒫(G) if and only if 〈u 〉⊂〈v à à or à u à ⊂ Ã
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Strong metric dimensions for power graphs of finite groups
TL;DR: In this article, the authors characterized the strong metric dimension of the order supergraph, the enhanced power graph and the reduced power graph of a finite group, and showed that for any finite group there exists a strong metric of order supergraphs with vertices whose vertices are adjacent if they generate cyclic subgroups.
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The strong metric dimension of the power graph of a finite group
TL;DR: The strong metric dimension of the power graph of a finite group is characterized and applications are considered as a cyclic group, an abelian group, a dihedral group or a generalized quaternion group.
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On the power graph of a finite group
TL;DR: In this article, the authors show that the power graph of a cyclic group has an transitive orientation and its core is a complete graph, and then they use the poset on all cyclic subgroups to characterise the structure of this power graph.
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On cyclic graphs of finite semigroups
TL;DR: In this article, the authors define and study the cyclic graph ΓS of a finite semigroup S and obtain some graph theoretical properties of the graph including its dominating number, independence number and genus.
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.