On the Kirchhoff index of some toroidal lattices.

The resistance distance is a novel distance function on a graph proposed by Klein and Randic [D.J. Klein and M. Randic, Resistance distance, J. Math. Chem. 12 (1993), pp. 81-85]. The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G. In this article, based on the result by Gutman and Mohar [I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), pp. 982-985], we compute the Kirchhoff index of the square, 8.8.4, hexagonal and triangular lattices, respectively. [ABSTRACT FROM AUTHOR]