TY - JOUR
ID - 13873
TI - On relation between the Kirchhoff index and number of spanning trees of graph
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Milovanovic, Igor
AU - Glogic, Edin
AU - Matejic, Marjan
AU - Milovanovic, Emina
AD - Faculty of Electronic Engineering, Nis, Serbia
AD - State University of Novi Pazar, Novi Pazar, Serbia
AD - Faculty of Electronic Engineering, Nis, Srbia
Y1 - 2020
PY - 2020
VL - 5
IS - 1
SP - 1
EP - 8
KW - Topological indices
KW - Kirchhoff index
KW - spanning trees
DO - 10.22049/cco.2019.26270.1088
N2 - 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 $G$.
UR - http://comb-opt.azaruniv.ac.ir/article_13873.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13873_db13742154db832474287f8d4db11c5f.pdf
ER -