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INCIDENCE SEMIRINGS OF GRAPHS AND VISIBLE BASES

Part of: Generalizations Multivariate analysis

Published online by Cambridge University Press:  12 September 2013

J. ABAWAJY ,
A. V. KELAREV ,
M. MILLER  and
J. RYAN
J. ABAWAJY
Affiliation:
School of Information Technology, Deakin University, 221 Burwood, Melbourne, Victoria 3125, Australia email jemal.abawajy@deakin.edu.au
A. V. KELAREV*
Affiliation:
School of Electrical Engineering and Computer Science, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia email Joe.Ryan@newcastle.edu.au
M. MILLER
Affiliation:
CARMA Priority Research Centre, School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia email Mirka.Miller@newcastle.edu.au Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic email Mirka.Miller@newcastle.edu.au
J. RYAN
Affiliation:
School of Electrical Engineering and Computer Science, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia email Joe.Ryan@newcastle.edu.au
*
✉andreikelarev-universityofnewcastle@yahoo.com
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Abstract

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We consider the incidence semirings of graphs and prove that every incidence semiring has convenient visible bases for its right ideals and for its left ideals, and that these visible bases can be used to determine the weights of all right ideals that have maximum weight and all left ideals that have maximum weight.

Keywords

incidence semiringsright idealsbalanced graphs

MSC classification

Secondary: 16Y60: Semirings 62H30: Classification and discrimination; cluster analysis
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 451 - 459
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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