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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Abawajy, J. Kelarev, A. V. Miller, M. and Ryan, J. 2016. Rees semigroups of digraphs for classification of data. Semigroup Forum, Vol. 92, Issue. 1, p. 121.

    Abawajy, J. Kelarev, A. V. Miller, M. and Ryan, J. 2015. Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications. Mathematics in Computer Science, Vol. 9, Issue. 2, p. 127.

  • Bulletin of the Australian Mathematical Society, Volume 89, Issue 3
  • June 2014, pp. 451-459


  • J. ABAWAJY (a1), A. V. KELAREV (a2), M. MILLER (a3) (a4) and J. RYAN (a2)
  • DOI:
  • Published online: 12 September 2013

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. Abawajy and A. V. Kelarev, ‘Classification systems based on combinatorial semigroups’, Semigroup Forum 86 (3) (2013), 603612.

J. S. Golan, Semirings and Their Applications (Kluwer Academic Publishers, Dordrecht, 1999).

A. V. Kelarev and D. S. Passman, ‘A description of incidence rings of group automata’, Contemp. Math. 456 (2008), 2733.

A. Kelarev, J. Ryan and J. Yearwood, ‘Cayley graphs as classifiers for data mining: the influence of asymmetries’, Discrete Math. 309 (17) (2009), 53605369.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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