Improved bounds for Kirchhoff index of graphs

Let G be a simple connected graph with n vertices. The Kirchhoff index of G is defined as Kf (G) = n Pni=1−1µ1i , where µ1 ≥ µ2 ≥ · · · ≥ µn−1 > µn = 0 are the Laplacian eigenvalues of G. Some bounds on Kf (G) in terms of graph parameters such as the number of vertices, the number of edges, first Zagreb index, forgotten topological index, etc., are presented. These bounds improve some previously known bounds in the literature.