On the kirchhoff index of graphs

Kinkar C. Das

doi:10.5560/ZNA.2013-0031

On the kirchhoff index of graphs

Kinkar C. Das

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

Let G be a connected graph of order n with Laplacian eigenvalues μ₁ ≥ μ₂ ≥...≥ μ_n-1 > μ_n = 0. The Kirchhoff index of G is defined as. 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

Original language	English
Pages (from-to)	531-538
Number of pages	8
Journal	Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Volume	68
Issue number	8-9
DOIs	https://doi.org/10.5560/ZNA.2013-0031
State	Published - 2013

Keywords

Graph spectrum
Kirchhoff index
Laplacian spectrum (of graph)
Nordhaus-gaddum-type

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10.5560/ZNA.2013-0031

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abstract = "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. 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",

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AB - 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. 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

KW - Graph spectrum

KW - Kirchhoff index

KW - Laplacian spectrum (of graph)

KW - Nordhaus-gaddum-type

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JF - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

IS - 8-9

ER -

On the kirchhoff index of graphs

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Keywords

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