A Lagrange series approach to the spectrum of the Kite graph

Piet Van Mieghem

doi:10.13001/1081-3810.3163

A Lagrange series approach to the spectrum of the Kite graph

Piet Van Mieghem

Network Architectures and Services

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

Abstract

A Lagrange series around adjustable expansion points to compute the eigenvalues of graphs, whose characteristic polynomial is analytically known, is presented. The computations for the kite graph P_nK_m, whose largest eigenvalue was studied by Stevanović and Hansen [D. Stevanović and P. Hansen. The minimum spectral radius of graphs with a given clique number. Electronic Journal of Linear Algebra, 17:110-117, 2008.], are illustrated. It is found that the first term in the Lagrange series already leads to a better approximation than previously published bounds.

Original language	English
Article number	59
Pages (from-to)	934-943
Number of pages	10
Journal	The Electronic Journal of Linear Algebra
Volume	30
DOIs	https://doi.org/10.13001/1081-3810.3163
Publication status	Published - 2015

Keywords

Characteristic polynomial
Lagrange series
Spectrum of a graph

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10.13001/1081-3810.3163

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abstract = "A Lagrange series around adjustable expansion points to compute the eigenvalues of graphs, whose characteristic polynomial is analytically known, is presented. The computations for the kite graph PnKm, whose largest eigenvalue was studied by Stevanovi{\'c} and Hansen [D. Stevanovi{\'c} and P. Hansen. The minimum spectral radius of graphs with a given clique number. Electronic Journal of Linear Algebra, 17:110-117, 2008.], are illustrated. It is found that the first term in the Lagrange series already leads to a better approximation than previously published bounds.",

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