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On the irregularity strength of the $$m\times n$$ grid. (English) Zbl 0771.05055
The irregularity strength of a graph $$G$$ is the minimum positive integer $$I(G)$$ such that positive integer weights $$\leq I$$ can be assigned to the edges of $$G$$ such that each vertex has a different weighted degree. The irregularity strength of the $$m\times n$$ grid is determined for many $$m$$ and $$n$$. In particular, for any positive integer $$d$$, the irregularity strength for all but a finite number of $$m\times n$$ grids with $$n-m=d$$ is determined. Intricate and interesting lower bound examples are described.

##### MSC:
 05C35 Extremal problems in graph theory 05C99 Graph theory
##### Keywords:
irregularity strength; grid; lower bound
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##### References:
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