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- W2023130429 abstract "Let G be a simple graph which has no connected components isomorphic to K1 or K2, and let Z+ be the set of positive integers. A function ω: E(G)→Z+ 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→∞ where q =|E(G)| and c1 is a constant depending only on G. An explicit expression for c1 is given. Analysis of this expression enables us to determine which graph with q edges has the least number of irregular assignments of strength at most λ, for λ sufficiently large." @default.
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- W2023130429 date "1991-11-01" @default.
- W2023130429 modified "2023-09-27" @default.
- W2023130429 title "On the number of irregular assignments on a graph" @default.
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- W2023130429 doi "https://doi.org/10.1016/0012-365x(91)90249-2" @default.
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