On the Spectrum of the Generalised Petersen Graphs

Adrian W. Dudek

doi:10.1007/s00373-016-1676-0

On the Spectrum of the Generalised Petersen Graphs

Adrian W. Dudek^*

^*Corresponding author for this work

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

Abstract

We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs P(n, k) tends to zero as n→ ∞. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs have poor expansion properties for large values of n. We also show that there is a positive proportion of the eigenvalues of P(n, k) tending to three.

Original language	English
Pages (from-to)	1843-1850
Number of pages	8
Journal	Graphs and Combinatorics
Volume	32
Issue number	5
DOIs	https://doi.org/10.1007/s00373-016-1676-0
Publication status	Published - 1 Sept 2016

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title = "On the Spectrum of the Generalised Petersen Graphs",

abstract = "We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs P(n, k) tends to zero as n→ ∞. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs have poor expansion properties for large values of n. We also show that there is a positive proportion of the eigenvalues of P(n, k) tending to three.",

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AB - We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs P(n, k) tends to zero as n→ ∞. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs have poor expansion properties for large values of n. We also show that there is a positive proportion of the eigenvalues of P(n, k) tending to three.

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On the Spectrum of the Generalised Petersen Graphs

Abstract

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