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 relations between power graphs and Cayley graphs
TL;DR: In this paper, Abawajy et al. showed that the vertex deleted subgraphs of some power graphs are spanning sub-graphs or equal to the complement of vertex deleted subsets of some unitary Cayley graphs of finite cyclic groups.
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Lambda number of the power graph of a finite group
TL;DR: In this article, the λ(2, 1)-labeling of a graph G is defined as the assignment of labels from nonnegative integers to all vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least 2 apart.
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Signless Laplacian spectrum of power graphs of finite cyclic groups
TL;DR: Using the theory of Equitable Partitions, the Signless Laplacian spectrum of power graph of Z n is completely determined for n = p q where p, q are distinct primes.
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Vertex connectivity of the power graph of a finite cyclic group II
Sriparna Chattopadhyay,Sriparna Chattopadhyay,Kamal Lochan Patra,Kamal Lochan Patra,Binod Kumar Sahoo,Binod Kumar Sahoo +5 more
TL;DR: The power graph as mentioned in this paper is a simple undirected graph whose vertices are the elements of a given finite group, in which two distinct vertices can be adjacent if and only if one of them can be obt...
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A combinatorial characterization of finite groups of prime exponent
TL;DR: The power graph of a group G is a simple and undirected graph with vertex set G and two distinct vertices are adjacent if one is a power of the other as discussed by the authors.
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.