度量化图的τ常数及其在图运算下的行为
The tau constant of a metrized graph and its behavior under graph operations
摘要：
本文研究了度量化图的一个重要不变量--τ常数，它在曲线的算术性质中有着重要的应用。我们给出了几个公式的τ常数，并显示它是如何变化的图形操作下，包括删除的边缘，收缩的边缘，和联盟的图形沿一个或两个点。我们展示了当一个图的边被任意图所取代时，τ常数是如何变化的。证明了Baker和Rumely关于几类度量化图的τ常数的下界猜想。
英文摘要：
This paper concerns the tau constant, which is an important invariant of a metrized graph, and which has applications to arithmetic properties of curves. We give several formulas for the tau constant, and show how it changes under graph operations including deletion of an edge, contraction of an edge, and union of graphs along one or two points. We show how the tau constant changes when edges of a graph are replaced by arbitrary graphs. We prove Baker and Rumely's lower bound conjecture on the tau constant for several classes of metrized graphs.
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