Browsing by Author "Cinkir, Zubeyir"

Now showing 1 - 6 of 6

Citation - WoS: 5
Citation - Scopus: 5
Admissible Invariants of Genus 3 Curves
(Springer Heidelberg, 2015) Cinkir, Zubeyir
Several 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.
An Extension of Lucas's Theorem
(indian Nat Sci Acad, 2025) Cinkir, Zubeyir; Ozturkalan, Aysegul
We give elementary proofs of some congruence criteria to compute binomial coefficients modulo a prime number. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas's Theorem by using those criteria. We give applications of these criteria by describing a method to derive identities and congruences involving sums of binomial coefficients.
Citation - WoS: 3
Citation - Scopus: 3
Computation of Polarized Metrized Graph Invariants by Using Discrete Laplacian Matrix
(Amer Mathematical Soc, 2015) 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.
Citation - WoS: 11
Citation - Scopus: 10
Contraction Formulas for the Kirchhoff and Wiener Indices
(Univ Kragujevac, Fac Science, 2016) Cinkir, Zubeyir
We relate the Kirchhoff index with some other metrized graph invariants. We establish several contraction formulas for the Kirchhoff index. We use these contraction formulas and certain edge densities to give new upper and lower bounds to the Kirchhoff index for any connected graph. As an another application of our contraction formulas when the graph is a tree, we derive new formulas as well as previously known formulas for the Wiener index with new proofs.
Citation - WoS: 24
Citation - Scopus: 26
Effective Resistances and Kirchhoff Index of Ladder Graphs
(Springer, 2016) Cinkir, Zubeyir
We 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.
Citation - WoS: 3
Citation - Scopus: 3
Families of Metrized Graphs With Small Tau Constants
(Springer Basel Ag, 2016) 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.