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Admissible invariants of genus 3 curves
(Springer New York LLC, 2015)
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 ...
Effective resistances and Kirchhoff index of ladder graphs
(SPRINGERONE NEW YORK PLAZA, SUITE 4600 , NEW YORK, NY 10004, UNITED STATES, 2016)
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 ...
Contraction Formulas for the Kirchhoff and Wiener Indices
(UNIV KRAGUJEVAC, FAC SCIENCEPO BOX 60, RADOJA DOMANOVICA 12, KRAGUJEVAC 34000, SERBIA, 2016)
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 ...
Families of Metrized Graphs with Small Tau Constants
(SPRINGER BASEL AGPICASSOPLATZ 4, BASEL 4052, SWITZERLAND, 2016)
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 ...
