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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Equality of various graphs on finite semigroups
Sandeep Dalal,Jitender Kumar +1 more
TL;DR: In this article, the authors consider various graphs, namely, power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup and classify finite semigroups such that the graphs in this pair are equal.
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Beck's Conjecture for Power Graphs
Himadri Mukherjee,Priya Das +1 more
TL;DR: In this paper, the authors answer the conjecture in complete generality and establish a "nicer" statement on a larger class of graphs, and clear up certain ambiguities present in the way the previous versions of the conjecture were posed.
On groups with chordal power graph, including a classification in the case of finite simple groups
Jendrik Brachter,Eda Kaja +1 more
TL;DR: In this article , the existence and non-existence of long cycles in power graphs of simple groups with chordal power graphs has been shown to be a property of chordal groups.
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The power index of a graph
TL;DR: In this paper, the power indices of complete graphs, complete bipartite graphs and $1$-factors are classified into power-critical and power-optimal groups.
On the tree-number of the power graph associated with a finite groups
TL;DR: In this article , the authors propose a solution to solve the problem of the problem: this article ] of "uniformity" and "uncertainty" of the solution.
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.