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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Some properties of various graphs associated with finite groups
TL;DR: In this article, the power graph and commuting graph associated with a finite group were investigated using their tree-numbers, and it was shown that the simple group $L_2(7)$ can be characterized through the tree-number of its power graph.
On the Difference Graph of power graphs of finite groups
TL;DR: For non-nilpotent groups, the dominating vertices of a graph D (G) of a symmetric group S n (or alternating group A n ) are a star graph, dominatable, split graph, chordal graph, threshold graph and cograph as mentioned in this paper .
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Hamiltonicity in power graphs of a class of abelian groups
TL;DR: In this article , the authors investigated the power graphs of a class of abelian groups and answer, in this case, the question whether or not the power graph is Hamiltonian.
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Power graphs of (non)orientable genus two
TL;DR: In this article, the authors classify finite groups whose power graphs have (non)orientable genus two and show that the power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other.
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Prime index elements graph of a group
TL;DR: In this paper , the authors define the (directed and undirected) prime index elements graph of a group G and study some interplay between the algebraic properties of group and graph theoretic properties.
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.