Anti-magic labelling of Cartesian product of graphs

  • Authors:

  • Yu-Chang Liang;Xuding Zhu

  • Affiliations:

  • Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan;Department of Mathematics, Zhejiang Normal University, China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

A graph G is anti-magic if there is a labelling of its edges with 1,2,...,|E| such that the sum of the labels assigned to edges incident to distinct vertices are different. In this paper, we prove that if G is k-regular for k=2, then for any graph H with |E(H)|=|V(H)|-1=1, the Cartesian product H@?G is anti-magic. We also show that if |E(H)|=|V(H)|-1 and each connected component of H has a vertex of odd degree, or H has at least 2|V(H)|-2 edges, then the prism of H is anti-magic.