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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]

The Wiener and Kirchhoff indices of a graph G are two of the most important topological indices in mathematical chemistry. A graph G is called to be a globular caterpillar if G is obtained from a complete graph Ks with vertex set {v1,v2,..., vs} by attaching ni pendent edges to each vertex vi of Ks for some positive integers s and n1,n2,...,ns, denoted by GCs;ni1s. Let GCs;n be the set of globular caterpillars GCs;ni1s with n vertices (n=s+∑i=1sni). In this article, we characterize the globular caterpillars with the minimal and maximal Wiener and Kirchhoff indices among GCs;n, respectively. [ABSTRACT FROM AUTHOR]