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3, is determined. A recent conjecture of Faudree et al. is disproved.
(15
and exhibit infinitely many sequences attaining equality. We also show 
doi:10.1016/0012-365X(91)90249-2 
Copyright © 1991 Published by Elsevier Science B.V. All rights reserved.
On the number of irregular assignments on a graph
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Gary Ebert, Joe Hemmeter, Felix Lazebnik* and Andrew Woldar**
Received 2 May 1989;
revised 26 September 1989.
Available online 25 March 2002.
Abstract
Let G be a simple graph which has no connected components isomorphic to K1 or K2, and let
+ be the set of positive integers. A function
is called an assignment on G, and for an edge e of G, ω(e) is called the weight of e. We say that w is of strength s if s = max{ω(e): e ε E(G)}. The weight of a vertex in G is defined to be the sum of the weights of its incident edges. We call assignment w irregular if distinct vertices have distinct weights. Let Irr(G,λ) be the number of irregular assignments on G with strength at most λ. We prove that
|Irr(G, λ) − λq+ c1λq−1|= O(λq−2), λ→∞
