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Ideal bases in constructions defined by directed graphs

Abawajy, J., Kelarev, A. and Ryan, J. 2015, Ideal bases in constructions defined by directed graphs, Electronic journal of graph theory and applications, vol. 3, no. 1, pp. 35-49, doi: 10.5614/ejgta.2015.3.1.5.

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Title Ideal bases in constructions defined by directed graphs
Author(s) Abawajy, J.
Kelarev, A.
Ryan, J.
Journal name Electronic journal of graph theory and applications
Volume number 3
Issue number 1
Start page 35
End page 49
Total pages 15
Publisher Institut Teknologi Bandung
Place of publication Jawa Barat, Indonesia
Publication date 2015
ISSN 2338-2287
Keyword(s) diagraphs
incidence semirings
two-sided ideals
visible bases
weights of ideals
Summary The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. Our main theorem establishes that, for every balanced digraph D and each idempotent semiring R with 1, the incidence semiring ID(R) of the digraph D has a convenient visible ideal basis BD(R). It also shows that the elements of BD(R) can always be used to generate two-sided ideals with the largest possible weight among the weights of all two-sided ideals in the incidence semiring.
Language eng
DOI 10.5614/ejgta.2015.3.1.5
Field of Research 080299 Computation Theory and Mathematics not elsewhere classified
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Grant ID DP0449469
Copyright notice ©2015, The Authors
Free to Read? Yes
Use Rights Creative Commons Attribution Share Alike licence
Persistent URL http://hdl.handle.net/10536/DRO/DU:30084456

Document type: Journal Article
Collections: School of Information Technology
Open Access Collection
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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.