The tau constant of a metrized graph and its behavior under graph operations

2009/01/05 by Zübeyir Çınkır, Cinkir, Zubeyir · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.0901.0407

openalex publication_date 2009/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The tau constant and the edge connectivity of a metrized graph

Cited by

• Zhang's Conjecture and the Effective Bogomolov Conjecture over function fields

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