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.
Field of Research
080599 Distributed Computing not elsewhere classified
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