# The tau constant of a metrized graph and its behavior under graph operations - Mathematics > Combinatorics

The tau constant of a metrized graph and its behavior under graph operations - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

Abstract: This paper concerns the tau constant, which is an important invariant of ametrized graph, and which has applications to arithmetic properties of curves.We give several formulas for the tau constant, and show how it changes undergraph operations including deletion of an edge, contraction of an edge, andunion of graphs along one or two points. We show how the tau constant changeswhen edges of a graph are replaced by arbitrary graphs. We prove Baker andRumely-s lower bound conjecture on the tau constant for several classes ofmetrized graphs.

Author: ** Zubeyir Cinkir**

Source: https://arxiv.org/