Rates of Convergence for the Embedding Distributions of Generalized Linear Graph Families
Sequences of genus polynomials for what became known as linear(or H-linear)families of graphs have been studied for more than 30 years.Most of previous papers concerning them aim to find recursions and expressions for genus(and Euler genus)polynomials of specific families,or try to prove the property of log-concavity.Recently,under some conditions,some researches reveal that the embedding distri-butions of generalized H-linear graph families {Gon} will tend to normal distributions when n tends to infinity(see[19]).Based on this previous work,in this article,we prove that the order of the convergence rate is1/√n.We also explain that,for the convergence rate obtained in this paper,it can been considered as optimal.In the end,we use some concrete examples to demonstrate our result.
rate of convergenceembedding distributionsH-linear family of graphsnormal distribution
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维普
