Ideal basis in constructions defined by directed graphs

Jemal Abawajy (Deakin University)
Andrei Kelarev (Deakin University University of Newcastle)
Joe Ryan (University of Newcastle)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 3, No 1 (2015): Electronic Journal of Graph Theory and Applications

The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication systems. Our main theorem establishes that, for every balanced digraph and each idempotent semiring with identity element, the incidence semiring of the digraph has a convenient visible ideal basis. It also shows that the elements of the basis can always be used to generate ideals with the largest possible weight among the weights of all ideals in the incidence semiring.