The Kirchhoff indices for circulant graphs

We present an approach yielding closed analytical formulas for the Kirchhoff indices of circulant graphs with even and odd vertex valency respectively and the prism-like graphs based on circulant graphs. Inspecting the asymptotics of the Kirchhoff index we show that in each of the above-mentioned cases the index can be expressed as the sum of a cubic polynomial and an exponentially vanishing remainder term.