%0 Journal Article
%T On relation between the Kirchhoff index and number of spanning trees of graph
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Milovanovic, Igor
%A Glogic, Edin
%A Matejic, Marjan
%A Milovanovic, Emina
%D 2020
%\ 06/01/2020
%V 5
%N 1
%P 1-8
%! On relation between the Kirchhoff index and number of spanning trees of graph
%K Topological indices
%K Kirchhoff index
%K spanning trees
%R 10.22049/cco.2019.26270.1088
%X Let $G$ 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 $G$.
%U http://comb-opt.azaruniv.ac.ir/article_13873_db13742154db832474287f8d4db11c5f.pdf