On Kirchhoff index and the number of spanning trees and rooted spanning forests in circulant graphs

The aim of this report is to find analytical formula for the Kirchhoff index and the number of spanning trees and rooted spanning forests in circulant graphs $C_n(s_1, s_2, ..., s_k)$ on $n$ vertices. Asymptotic behavior of the above mentioned quantities is investigated as $n$ tends to the infinity. We proof that Kirchhoff index of a circulant graph can be expressed as a sum of a cubic polynomial of $n$ and an exponentially small remainder.