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
Citations
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Total graphs of polynomial rings and rings of fractions
TL;DR: The total graph of R, denoted by T(Γ(R)), is a graph with all elements of R as vertices, and two distinct vertices x, y are adjacent if and only if x + y ∈ Z(R), wh...
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On finite groups whose power graph is a cograph
TL;DR: In this article, it was shown that the power graph of a power power graph is a cograph for groups whose orders are prime or the product of two (possibly equal) primes.
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Extended zero divisor graph on commutative semigroup
Mohammad Ashraf,Mohit Kumar +1 more
TL;DR: In this article, the extended zero divisor graph EG(S) associated to a commutative semigroup S with zero was studied, and the authors characterized all extended zero-divisor graphs with three vertices.
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On Distribution of Laplacian Eigenvalues of Graphs
TL;DR: In this paper, the Laplacian eigenvalues of graphs and Brouwer's conjecture for trees have been investigated, and it is shown that the star graph has minimum generalized distance energy among all trees.
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On groups with specified quotient power graphs
TL;DR: In this article, the relation between the power and quotient power graphs of a finite group was studied and some interesting graph theoretical properties of the quotient and power graphs were found.
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.