Z. Naturforsch. 68a, 531 – 538 (2013)
On the Kirchhoff Index of Graphs
Kinkar C. Das
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
Received December 20, 2012 / revised March 15, 2013 / published online May 22, 2013
Reprint requests to: K. C. D.; E-mail: kinkardas2003@googlemail.com
Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥…≥ μn−1 > μn = 0. The Kirchhoff index of G is defined as Kf = Kf(G) = n ∑k=1n−11/μk.

In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus–Gaddum-type result for the Kirchhoff index.

Key words: Graph Spectrum; Laplacian Spectrum (of Graph); Kirchhoff Index; Nordhaus–Gaddum-Type.
Mathematics Subject Classification 2000: 05C50; 15A18
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