@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 $G$ be a simple connected graph with degree sequence $(d_1,d_2,\ldots, d_n)$ where $\Delta =d_1\geq d_2\geq\cdots\geq d_n=\delta >0$ and let $\mu_1\geq \mu_2\geq\cdots\geq\mu_{n-1}>\mu_n=0$ be the Laplacian eigenvalues of $G$. Let $Kf(G)=n\sum_{i=1}^{n-1} \frac{1}{\mu_i}$ 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 $G$.},
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}
}