### 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 language | English |
---|---|

Pages (from-to) | 355-374 |

Number of pages | 20 |

Journal | Journal of Graph Theory |

Volume | 16 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1992 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*16*(4), 355-374. https://doi.org/10.1002/jgt.3190160409