Automorphism groups of supergraphs of the power graph of a finite group
Asma Hamzeh,Ali Reza Ashrafi +1 more
Reads0
Chats0
TLDR
It is proved that the automorphism group of the main supergraphs and cyclic graphs can be written as a combination of Cartesian and wreath products of some symmetric groups.About:
This article is published in European Journal of Combinatorics.The article was published on 2017-02-01 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Inner automorphism & Graph automorphism.read more
Citations
More filters
Journal ArticleDOI
Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups
Asma Hamzeh,Ali Ashrafi Reza +1 more
TL;DR: In this paper, the characteristic polynomial of the power graph for dihedral, semi-dihedral, cyclic and dicyclic groups was computed and the spectrum and Laplacian spectrum of these graphs were computed.
Journal ArticleDOI
On the enhanced power graph of a finite group
TL;DR: In this article, the minimum degree, indescrete power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup.
Journal ArticleDOI
On the Connectivity of Enhanced Power Graphs of Finite Groups
TL;DR: In this article, the vertex connectivity of enhanced power graphs of finite groups was studied and an upper bound for vertex connectivity was derived for any general abelian group G. The vertex connectivity for the enhanced power graph of any general group G is given.
Posted Content
Laplacian spectra of power graphs of certain finite groups
TL;DR: It is proved that the notion of equality of the vertex connectivity and the algebraic connectivity andThe notion of Laplacian integral are equivalent for power graphs of dicyclic groups.
Posted Content
On the connectivity of enhanced power graph of finite group
TL;DR: An upper bound of vertex connectivity is derived for the enhanced powergraph of any general abelian group G, such that the proper enhanced power graph is connected.
References
More filters
Book
Introduction to Graph Theory
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Journal ArticleDOI
Undirected power graphs of semigroups
TL;DR: In this article, it was shown that the multiplicative semigroup ℤn and its subgroup Un is complete if and only if n = 1,2,4,p or 2p, where p is a Fermat prime.
Journal ArticleDOI
The power graph of a finite group
Peter J. Cameron,Shamik Ghosh +1 more
TL;DR: It is conjectured that two finite groups with isomorphic power graphs have the same number of elements of each order, and that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4.
Journal ArticleDOI
Directed Graphs and Combinatorial Properties of Semigroups
Andrei V. Kelarev,Stephen Quinn +1 more
TL;DR: In this paper, a complete description of all commutative semigroups satisfying three other combinatorial properties defined in terms of directed graphs is given, by a graph we mean a directed graph without loops or multiple edges.