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
Citations
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The metric dimension of the enhanced power graph of a finite group
Xuanlong Ma,Yanhong She +1 more
TL;DR: The enhanced power graph of a finite group G is the graph whose vertex set is G, and two distinct vertices are adjacent if they generate a cyclic subgroup of G as mentioned in this paper.
Journal ArticleDOI
Vertex connectivity of the power graph of a finite cyclic group
TL;DR: A new upper bound is given for the vertex connectivity of $\kappa(\mathcal{P}(C_n)$ and it is determined when $n$ is a product of distinct prime numbers.
Posted Content
The rainbow connection number of the power graph of a finite group
TL;DR: In this article, the authors studied the rainbow connection number of the power graph of a finite group and showed that the number is at most three if the group has no maximal involutions.
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An Euler totient sum inequality
TL;DR: In this article, the clique number of the power graph of a finite cyclic group and the significance of the inequality in this context were discussed. But the interpretation of χ as a clique was not discussed.
Journal ArticleDOI
On the Connectivity and Independence Number of Power Graphs of Groups
TL;DR: All groups whose power graphs have finite independence number are characterized, and it is shown that they have clique cover number equal to their independence number, and this number is calculated.
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.