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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The number of spanning trees of power graphs associated with specific groups and some applications
TL;DR: The number of spanning trees of the power graph associated with specific finite groups is found and the alternating group $\mathbb{A}_5$ is uniquely determined by tree-number of its power graph among all finite simple groups.
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Co-Prime Order graph of a finite abelian Group and Dihedral Group
Amit Sehgal,Manjeet,Dalip Singh +2 more
TL;DR: In this paper, the degree of a vertex in the Co-Prime Order graph of a finite abelian group or a dihedral group was investigated. And the Laplacian spectrum of the co-prime order graph was also investigated.
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The Power Graph of a Torsion-Free Group of Nilpotency Class $2$
TL;DR: In this article, it was proved that the power graph by any of the three versions of the definitions determines the other two up to isomorphism up to the point of being isomorphic.
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Forbidden subgraphs of power graphs
TL;DR: The undirected power graph (or simply power graph) of a group is a graph whose vertices are the elements of the group, in which two vertices $u$ and $v$ are connected by an edge between if and only if either $u=v^i$ or $v=u^j$ for some $i$, $j$.
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Laplacian spectrum of reduced power graph of certain finite groups
R. Rajkumar,T. Anitha +1 more
TL;DR: The reduced power graph of a group G is the graph whose vertices are the elements of G and two vertices u and v are adjacent if and only if u⊆v or v⊂u as mentioned in this paper.
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.