Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
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Article Citation - WoS: 3Citation - Scopus: 3Families of Metrized Graphs With Small Tau Constants(Springer Basel Ag, 2016-01-23) Cinkir, ZubeyirBaker 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.Article Citation - WoS: 26Citation - Scopus: 27Effective Resistances and Kirchhoff Index of Ladder Graphs(Springer, 2016-01-21) Cinkir, ZubeyirWe explicitly compute the effective resistances between any two vertices of a ladder graph by using circuit reductions. Using our findings, we obtain explicit formulas for Kirchhoff index of a ladder graph. Comparing our formula for Kirchhoff index and previous results in the literature, we obtain an explicit sum formula involving trigonometric functions. We also expressed our formulas in terms of certain generalized Fibonacci numbers that are the values of the Chebyshev polynomials of the second kind at 2.Article Citation - WoS: 6Citation - Scopus: 6Admissible Invariants of Genus 3 Curves(Springer Heidelberg, 2015-06-03) Cinkir, ZubeyirSeveral invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we explicitly calculated these admissible invariants for all curves of genus 3. We find the sharp lower bound for the invariants phi, lambda and epsilon for all polarized metrized graphs of genus 3. This improves the lower bound given for Effective Bogomolov Conjecture for such curves.