7 citations · 22 across the 19 of their papers we have counts for
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The Number of Spanning Trees for The Generalized Cones of , The Generalized Half Cones of and Some Family of Modified
Zubeyir Cinkir
We compute the total number of spanning trees for the generalized cone of the complete graph and a number of families of some modified bipartite graphs . In particul…
Explicit Rayleigh's Principles for Resistive Electrical Network and The Total Number of Spanning Trees of Graphs
Zubeyir Cinkir
We give identities for the voltage and resistance functions on a metrized graph to show how these functions behave under any edge deletion/contraction and the identification of any…
Effective Resistances and Kirchhoff index of Prism Graphs
Zubeyir Cinkir
We explicitly compute the effective resistances between any two vertices of a prism graph by using circuit reductions and our earlier findings on a ladder graph. As an application,…
Effective Resistances, Kirchhoff index and Admissible Invariants of Ladder Graphs
Zubeyir Cinkir
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 Kirchhof…
Families of Metrized Graphs With Small Tau Constants
Zubeyir Cinkir
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 con…
Contraction Formulas For Kirchhoff And Wiener Indices
Zubeyir Cinkir
We establish several contraction formulas for Kirchhoff index. We relate Kirchhoff index with some other metrized graph invariants. By applying our contraction formulas successivel…