Abstract Let G be a graph and let be its edge ideal. When G is unicyclic, we give a decomposition of symbolic powers of I in terms of its ordinary powers. This allows us to explicitly compute the Waldschmidt constant and the resurgence number of I. When G is an odd cycle, we explicitly compute the regularity of for all In doing so, we also give a natural lower bound for the regularity function for for an arbitrary graph G.

中文翻译：

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图的边理想的符号幂

Abstract 设 G 为图，并设其边理想。当 G 是单环时，我们根据它的普通幂给出 I 的符号幂的分解。这允许我们显式计算 Waldschmidt 常数和 I 的回潮数。 当 G 是奇数循环时，我们显式计算 for all 的正则性这样做，我们还为任意一个正则函数给出了自然下界图 G。