Power graphs: A survey
Jemal H. Abawajy,Andrei V. Kelarev,Morshed U. Chowdhury +2 more
- Vol. 1, Iss: 2, pp 125-147
TLDR
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
More filters
Journal ArticleDOI
Trees whose regular endomorphisms form a monoid
Rui Gu,Hailong Hou +1 more
TL;DR: Conditions under which the regular endomorphisms of the tree form a monoid are given and it is given that the tree T is a monoids.
Journal ArticleDOI
Exchange property for resolving sets in power graphs
Junyao Pan,Xiuyun Guo +1 more
TL;DR: It is shown that the resolving sets do not have exchange property in the power graph of the symmetric group S n if and only if n = 2 + p where p is a prime with p > 3 .
Journal ArticleDOI
On Distance Laplacian Spectra of Certain Finite Groups
Journal ArticleDOI
Spectrum of proper power graphs of the direct product of certain finite groups
TL;DR: The proper power graph P∗(G) of a group G is the simple graph with non-trivial elements of G as vertices and two distinct elements are adjacent if and only if one is a power of the other as mentioned in this paper.
Journal ArticleDOI
Finite groups with star-free noncyclic graphs
TL;DR: In this paper, the authors classify all finite noncyclic groups whose non-cyclic graphs are k-1,n-free, where k is the number of vertices in the graph.
References
More filters
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.