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The irregularity strength of $$tK_ p$$. (English) Zbl 0834.05029
The irregularity strength of a simple graph is the smallest integer for which the edges may be assigned weights not exceeding it, such that the weight sums of adjacent edges are different at all vertices. A general formula is obtained for the irregularity strength of disjoint unions of identical complete graphs.

##### MSC:
 05C35 Extremal problems in graph theory 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 11P99 Additive number theory; partitions
##### Keywords:
irregular networks; irregularity strength; weight sums
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##### References:
 [1] Chartrand, G.; Jacobson, M.S.; Lehel, J.; Oellermann, O.R.; Ruiz, S.; Saba, F., Irregular networks, (), 187-192 [2] Dinitz, J.H.; Garnick, D.K.; Gyárfás, A., On the irregularity strength of the m × n grid, J. graph theory, 16, 355-374, (1992) · Zbl 0771.05055 [3] Faudree, R.J.; Jacobson, M.S.; Kinch, L.; Lehel, J., Irregularity strength of dense graphs, Discrete math., 91, 45-59, (1991) · Zbl 0755.05092 [4] Faudree, R.J.; Jacobson, M.S.; Lehel, J.; Schelp, R.H., Irregular networks, regular graphs and integer matrices with distinct row and column sums, Discrete math., 76, 223-240, (1989) · Zbl 0685.05029 [5] Lehel, J., Facts and quests on degree irregular assignments, (), 765-782 · Zbl 0841.05052
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