Chapter

Combinatorial Algorithms

Volume 8288 of the series Lecture Notes in Computer Science pp 376-387

An Application of Completely Separating Systems to Graph Labeling

  • Leanne RylandsAffiliated withSchool of Computing, Engineering and Mathematics, University of Western Sydney
  • , Oudone PhanalasyAffiliated withSchool of Mathematical and Physical Sciences, University of NewcastleDepartment of Mathematics, National University of Laos
  • , Joe RyanAffiliated withSchool of Electrical Engineering and Computer Science, University of Newcastle
  • , Mirka MillerAffiliated withSchool of Mathematical and Physical Sciences, University of NewcastleDepartment of Mathematics, University of West BohemiaDepartment of Informatics, King’s College LondonDepartment of Mathematics, ITB Bundung

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Abstract

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.

Keywords

completely separating system antimagic labeling non-regular graph