On the irregularity strength of the m × n grid

Jeffrey H. Dinitz, David K. Garnick, A. Gyárfás

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Abstract

Given a graph G with weighting w: E(G) ← Z+, the Strength of G(w) is the maximum weight on any edge. The sum of a vertex in G(w) is the sum of the weights of all its incident edges. The network G(w) is irregular if the vertex sums are distinct. The irregularity strength of G is the minimum strength of the graph under all irregular weightings. In this paper we determine the irregularity strength of the m × n grid for certain m and n. In particular, for every positive integer d we find the irregularity strength for all but a finite number of m × n grids where n ‐ m = d. In addition, we present a general lower bound for the irregularity strength of graphs. © 1992 John Wiley & Sons, Inc.

Original languageEnglish
Pages (from-to)355-374
Number of pages20
JournalJournal of Graph Theory
Volume16
Issue number4
DOIs
Publication statusPublished - 1992

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ASJC Scopus subject areas

  • Geometry and Topology

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