Abstract:
Let $G$ be a finite connected graph on $n$ vertices with Laplacian spectrum
$0=\lambda_1<\lambda_2\le\ldots\le\lambda_n.$ The Kirchhoff index of $G$ is defined by the formula
$$Kf(G)=n\sum\limits_{j=2}^n\frac{1}{\lambda_j}.$$ The aim of this paper is to find an explicit analytical
formula for the Kirchhoff index of Möbius ladder graph $M_n=C_{2n}(1,n)$ and Prism graph $Pr_n=C_n\times P_2$.
The obtained formulas provide a simple asymptotical behavior of both invariants as $n$ is going to the infinity.
Keywords:Laplacian matrix, circulant graph, Kirchhoff index, Wiener index, Chebyshev polynomial.