@article {
author = {Milovanovic, Igor and Glogic, Edin and Matejic, Marjan and Milovanovic, Emina},
title = {On relation between the Kirchhoff index and number of spanning trees of graph},
journal = {Communications in Combinatorics and Optimization},
volume = {5},
number = {1},
pages = {1-8},
year = {2020},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26270.1088},
abstract = {Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ 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 $Delta$.},
keywords = {Topological indices,Kirchhoff index,spanning trees},
url = {http://comb-opt.azaruniv.ac.ir/article_13873.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13873_db13742154db832474287f8d4db11c5f.pdf}
}