Lucky labelings of graphs

  • Authors:

  • Sebastian Czerwiński;Jarosław Grytczuk;Wiktor Żelazny

  • Affiliations:

  • Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, Poland;Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, 30-387 Kraków, Poland;Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, 30-387 Kraków, Poland

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

Suppose the vertices of a graph G were labeled arbitrarily by positive integers, and let S(v) denote the sum of labels over all neighbors of vertex v. A labeling is lucky if the function S is a proper coloring of G, that is, if we have S(u)S(v) whenever u and v are adjacent. The least integer k for which a graph G has a lucky labeling from the set {1,2,...,k} is the lucky number of G, denoted by @h(G). Using algebraic methods we prove that @h(G)=