Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285120200601On relation between the Kirchhoff index and number of spanning trees of graph181387310.22049/cco.2019.26270.1088ENIgorMilovanovicFaculty of Electronic Engineering, Nis, SerbiaEdinGlogicState University of Novi Pazar, Novi Pazar, SerbiaMarjanMatejicFaculty of Electronic Engineering, Nis, SrbiaEminaMilovanovicFaculty of Electronic Engineering, Nis, SerbiaJournal Article20180604Let $G$ be a simple connected graph with degree sequence $(d_1,d_2,ldots, d_n)$ where $Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and let $mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$ be the Laplacian eigenvalues of $G$. Let $Kf(G)=nsum_{i=1}^{n-1} frac{1}{mu_i}$ and $tau(G)=frac 1n prod_{i=1}^{n-1} mu_i$ denote the Kirchhoff index and the number of spanning trees of $G$, respectively. In this paper we establish several lower bounds for $Kf(G)$ in terms of $tau(G)$, the order, the size and maximum degree of $G$.http://comb-opt.azaruniv.ac.ir/article_13873_db13742154db832474287f8d4db11c5f.pdf