An Application of Completely Separating Systems to Graph Labeling

  • Leanne Rylands
  • Oudone Phanalasy
  • Joe Ryan
  • Mirka Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8288)


In this paper a known algorithm used for the construction of completely separating systems (CSSs), Roberts’ Construction, is modified and used in a variety of ways to build CSSs. The main interest is in CSSs with different block sizes. A connection between CSSs and vertex antimagic edge labeled graphs is then exploited to prove that various non-regular graphs are antimagic. An outline for an algorithm which produces some of these non-regular graphs together with a vertex antimagic edge labeling is presented.


completely separating system antimagic labeling non-regular graph 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Leanne Rylands
    • 1
  • Oudone Phanalasy
    • 2
    • 3
  • Joe Ryan
    • 4
  • Mirka Miller
    • 2
    • 5
    • 6
    • 7
  1. 1.School of Computing, Engineering and MathematicsUniversity of Western SydneySydneyAustralia
  2. 2.School of Mathematical and Physical SciencesUniversity of NewcastleNewcastleAustralia
  3. 3.Department of MathematicsNational University of LaosVientianeLaos
  4. 4.School of Electrical Engineering and Computer ScienceUniversity of NewcastleNewcastleAustralia
  5. 5.Department of MathematicsUniversity of West BohemiaPilsenCzech Republic
  6. 6.Department of InformaticsKing’s College LondonLondonUK
  7. 7.Department of MathematicsITB BundungBundungIndonesia

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