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Citation - WoS: 3
Citation - Scopus: 3
Families of Metrized Graphs With Small Tau Constants
(Springer Basel Ag, 2016-01-23) Cinkir, Zubeyir
Baker and Rumely's tau lower bound conjecture claims that if the tau constant of a metrized graph is divided by its total length, this ratio must be bounded below by a positive constant for all metrized graphs. We construct several families of metrized graphs having small tau constants. In addition to numerical computations, we prove that the tau constants of the metrized graphs in one of these families, the hexagonal nets around a torus, asymptotically approach to 108 which is our conjectural lower bound.
Citation - WoS: 3
Citation - Scopus: 3
Computation of Polarized Metrized Graph Invariants by Using Discrete Laplacian Matrix
(Amer Mathematical Soc, 2015-05-08) Cinkir, Zubeyir
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry have been studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. The algorithm we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms.

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