An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

Variants of finite full transformation semigroups

The variant of a semigroup S with respect to an element a in S, denoted S^a, is the semigroup with underlying set S and operation * defined by x*y=xay for x,y in S. In this article, we study variants T_X^a of the full transformation semigroup T_X on a finite set X. We explore the structure of T_X^a as well as its subsemigroups Reg(T_X^a) (consisting of all regular elements) and E_X^a (consisting of all products of idempotents), and the ideals of Reg(T_X^a). Among other results, we calculate the rank and idempotent rank (if applicable) of each semigroup, and (where possible) the number of (idempotent) generating sets of the minimal possible size.Comment: 25 pages, 6 figures, 1 table - v2 includes a couple more references - v3 changes according to referee comments (to appear in IJAC

The semidirectly closed pseudovariety generated by aperiodic Brandt semigroups

This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup $B_2$, denoted $\mathbf V^*(B_2)$. We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by $B_2$ which leads to the main result, which states that $\mathbf V^*(B_2)$ is decidable. Independently, using some suggestions given by J.~Almeida in his book ``Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in $\mathbf V^*(B_2)$.Centro de Matemática da Universidade do Minho (CMAT). Fundação para a Ciência e a Tecnologia (FCT) - Praxis/2/2.1/MAT/63/94

An Algebraic Characterisation of Concurrent Composition

We give an algebraic characterization of a form of synchronized parallel composition allowing for true concurrency, using ideas based on Peter Landin's "Program-Machine Symmetric Automata Theory".Comment: This is an old technical report from 1981. I submitted it to a special issue of HOSC in honour of Peter Landin, as explained in the Prelude, added in 2008. However, at an advanced stage, the handling editor became unresponsive, and the paper was never published. I am making it available via the arXiv for the same reasons given in the Prelud