ELECTRONIC JOURNAL OF COMBINATORICS, cilt.18, 2011 (SCI İndekslerine Giren Dergi)
This paper concerns the tau constant, which is an important in variant 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.