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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Cayley-symmetric semigroups
TL;DR: In this article, the concept of Cayley-symmetric semigroups is introduced, and several equivalent conditions of a Cayley symmetric semigroup are given so that an open problem proposed by Zhu [19] is resolved generally.
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On spectra and spectral radius of Signless Laplacian of power graphs of some finite groups
TL;DR: Lower and upper bounds on ρ(Q(Q(𝒫(ℤn))) for any n > 0 are given in this article. But the upper bound is not known.
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Some results in a new power graphs in finite groups
TL;DR: The power graph of a group is the graph whose vertex set is the set of non-trivial elements of group, two elements being adjacent if one is a power of the other as mentioned in this paper.
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On normalized Laplacian eigenvalues of power graphs associated to finite cyclic groups
TL;DR: In this paper , the normalized Laplacian eigenvalues of the joined union of regular graphs in terms of the adjacency eigenvalue and the eigen values of quotient matrix associated with graph G were investigated.
Cayley graph associated to a semihypergroup
TL;DR: In this paper, a Cayley graph associated to a semihypergroup (or hypergroup) is studied, and the properties of this graph are investigated, such as Hamiltonian cycles in this graph.
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.