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Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications

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Abstract

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

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Authors and Affiliations

  1. School of Information Technology, Deakin University, 221 Burwood, Melbourne, VIC, 3125, Australia

    J. Abawajy & A. V. Kelarev

  2. School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    A. V. Kelarev

  3. CARMA Priority Research Centre, School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    M. Miller

  4. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    M. Miller

  5. School of Electrical Engineering and Computer Science, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    J. Ryan

Authors
  1. J. Abawajy
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  2. A. V. Kelarev
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  3. M. Miller
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  4. J. Ryan
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Correspondence to J. Ryan.

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Abawajy, J., Kelarev, A.V., Miller, M. et al. Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications. Math.Comput.Sci. 9, 127–137 (2015). https://doi.org/10.1007/s11786-015-0217-1

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  • DOI: https://doi.org/10.1007/s11786-015-0217-1

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