Author/Authors :
Milovanovic, Igor Faculty of Electronic Engineering, Nis, Serbia , Glogic, Edin State University of Novi Pazar, Novi Pazar, Serbia , Matejic, Marjan Faculty of Electronic Engineering, Nis, Serbia , Emina Milovanovic Faculty of Electronic Engineering, Nis, Serbia
Abstract :
Let G be a simple connected graph with degree sequence (d1; d2; : : : ; dn)
where Δ = d1 ≥ d2 ≥ ... ≥ dn = δ > 0 and let μ1 ≥ μ2 . . . . μn≥1 > μn = 0 be the
Laplacian eigenvalues of G. Let Kf(G) = n
PnΣ1
i=1
1
i
and Τ(G) = 1
n
Qn1
i=1 μi 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 Τ(G), the order, the size and
maximum degree of G.
