On a relationship between completely separating systems and antimagic labeling of regular graphs

  • Authors:

  • Oudone Phanalasy;Mirka Miller;Leanne Rylands;Paulette Lieby

  • Affiliations:

  • School of Electrical Engineering and Computer Science, The University of Newcastle, NSW, Australia and Department of Mathematics, National University of Laos, Vientiane, Laos;School of Electrical Eng. and Comp. Science, The Univ. of Newcastle, NSW, Australia and Dept. of Mathematics, Univ. of West Bohemia, Pilsen, Czech Republic and Dept. of Computer Science, King's Co ...;School of Computing and Mathematics, University of Western Sydney, NSW, Australia;NICTA, Canberra ACT, Australia

  • Venue:
  • IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
  • Year:
  • 2010

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Abstract

A completely separating system (CSS) on a finite set [n] is a collection C of subsets of [n] in which for each pair a ≠ b ∈ [n], there exist A, B ∈ C such that a ∈; A, b ∉ A and b ∈ B, a ∉ B. An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs.