Title of article :
Ideal bases in constructions defined by directed graphs
Author/Authors :
Abawajy, J. Deakin University - School of Information Technology, Australia , Kelarev, A.V. University of Newcastle - CARMA Priority Research Center, School of Mathematical and Physical Sciences, Australia , Kelarev, A.V. Deakin University - School of Information Technology, Australia , Ryan, J. University of Newcastle - School of Electrical Engineering and Computer Science, Australia
Abstract :
The present article continues the investigation of visible ideal bases in constructions defined usingdirected graphs. Our main theorem establishes that, for every balanced digraph D and eachidempotent semiring R with 1, the incidence semiring ID(R) of the digraph D has a convenientvisible ideal basis BD(R). It also shows that the elements of BD(R) can always be used to generatetwo-sided ideals with the largest possible weight among the weights of all two-sided ideals in theincidence semiring.
Keywords :
digraphs , incidence semirings , two , sided ideals , visible bases , weights of ideals
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
