L(2, 1)-labeling of direct product of paths and cycles

  • Authors:

  • Pranava K. Jha;Sandi Klavžar;Aleksander Vesel

  • Affiliations:

  • Department of Computer Science, St. Cloud State University, St. Cloud, MN;Department of Mathematics and Computer Science, PeF, University of Maribor. Koroška cesta 160, 2000 Maribor, Slovenia;Department of Mathematics and Computer Science, PeF, University of Maribor. Koroška cesta 160, 2000 Maribor, Slovenia

  • Venue:
  • Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
  • Year:
  • 2005

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Abstract

An L (2, 1)-labeling of a graph G is an assignment of labels from {0, 1,....., λ} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. The λ-number λ(G) of G is the minimum value λ such that G admits an L (2, 1)-labeling. Let G × H denote the direct product of G and H. We compute the λ-numbers for each of C7i × C7j, C11i × C11j × C11k, P4 × Cm, and P5 × Cm. We also show that for n ≥ 6 and m ≥ 7, λ(Pn × Cm) = 6 if and only if m = 7k, k ≥ 1. The results are partially obtained by a computer search.