Geodesic
Remarks on the Degree Kirchhoff Index
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 15

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Let $G$ be a simple connected graph with $n$ vertices and $m$ edges, with normalized Laplacian eigenvalues $\rho_1\geq \rho_2\geq \cdots\geq \rho_{n-1}>\rho_n=0$. The degree Kirchhoff index $Kf^{\ast}(G)$ is defined as $Kf^{\ast}(G)=2m \sum_{i=1}^{n-1}\frac{1}{\rho_{i}}$. In this paper we obtain lower and upper bounds for $Kf^{\ast}(G)$.
Classification : 05C12 05C50
Keywords: Degree Kirchhoff index, Laplacian eigenvalues (of graph), vertex degree 
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M. Matejić; I. Milovanović; E. Milovanović. Remarks on the Degree Kirchhoff Index. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 15 . http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a1/