Directed Graphs and Combinatorial Properties of Semigroups
Andrei V. Kelarev,Stephen Quinn +1 more
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TLDR
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.About:
This article is published in Journal of Algebra.The article was published on 2002-05-01 and is currently open access. It has received 198 citations till now. The article focuses on the topics: Semigroup & Directed graph.read more
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The structure of Leavitt path algebras and the Invariant Basis Number property
T. G. Nam,N.T. Phuc +1 more
TL;DR: In this article, the structure of the Leavitt path algebra of a finite graph via some step-by-step process of source eliminations is provided, and a matrix-theoretic criterion for the linearity of a path algebra having invariant basis number is given.
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On the power graph of a finite group
TL;DR: In this article, the authors show that the power graph of a cyclic group has an transitive orientation and its core is a complete graph, and then they use the poset on all cyclic subgroups to characterise the structure of this power graph.
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On cyclic graphs of finite semigroups
TL;DR: In this article, the authors define and study the cyclic graph ΓS of a finite semigroup S and obtain some graph theoretical properties of the graph including its dominating number, independence number and genus.
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The Power Graph of a Torsion-Free Group Determines the Directed Power Graph
TL;DR: Any two torsion-free groups having isomorphic power graphs have isomorphic directed power graphs, which generalizes the results of Cameron, Guerra and Jurina.
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On the Cayley \(\mathcal {D}\)-saturated property of semigroups
TL;DR: In this paper, the Cayley-saturated property of product semigroups and semilattice of semigroup was studied in the context of product semiigroups.
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
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.
Book
Combinatorics on words
TL;DR: Perrin and Perrin this article showed that square free words and idempotent semigroups can be expressed in terms of free monoids, and the critical factorization theorem of Van der Waerden's theorem.
BookDOI
Handbook of Formal Languages
Grzegorz Rozenberg,Arto Salomaa +1 more
TL;DR: This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field.