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 $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,<br />be a simple connected graph,<br /> with sequence of vertex degrees<br />$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues<br />$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}<br />frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning trees of $G$, respectively. In this paper we determine several lower bounds for $Kf(G)$ depending on $t(G)$ and some of the graph parameters $n$, $m$, or $Delta$.http://comb-opt.azaruniv.ac.ir/article_13873_db13742154db832474287f8d4db11c5f.pdf