Kirchhoff index and degree Kirchhoff index of complete multipartite graphs

Given a complete multipartite graph G, we explicitly formulate the effective resistance distance between any two vertices of G, using methods from linear algebra. The Kirchhoff index and the degree Kirchhoff index are defined in terms of the effective resistance distances for any simple graph. In this paper, for G, the exact formulae for the two indices are provided. Along with these results, we obtain the optimal Kirchhoff index and the optimal degree Kirchhoff index.