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    • Contraction Formulas for the Kirchhoff and Wiener Indices 

      Cinkir, Zubeyir (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 ...
    • Effective resistances and Kirchhoff index of ladder graphs 

      Cinkir, Zubeyir (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 ...
    • Families of Metrized Graphs with Small Tau Constants 

      Cinkir, Zubeyir (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 ...