Rees semigroups of digraphs for classification of data

Recent research has motivated the investigation of the weights of ideals in semiring constructions based on semigroups. The present paper introduces Rees semigroups of directed graphs. This new construction is a common generalization of Rees matrix semigroups and incidence semigroups of digraphs. For each finite subsemigroup S of the Rees semigroup of a digraph and for every zero-divisor-free idempotent semiring F with identity element, our main theorem describes all ideals J in the semigroup semiring F0[S] such that J has the largest possible weight.

A Grobner-Shirshov algorithm for applications in internet security

The design of multiple classification and clustering systems for the detection of malware is an important problem in internet security. Grobner-Shirshov bases have been used recently by Dazeley et al. [15] to develop an algorithm for constructions with certain restrictions on the sandwich-matrices. We develop a new Grobner Shirshov algorithm which applies to a larger variety of constructions based on combinatorial Rees matrix semigroups without any restrictions on the sandwich matrices.

Power graphs : a survey

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.