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{\bf Zubeyir Cinkir}
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{\bf The Tau Constant of a Metrized Graph and its Behavior under Graph Operations}
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This paper concerns the tau constant, which is an important invariant
of a metrized graph, and which has applications to arithmetic
properties of algebraic 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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