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On the Spectrum of the Generalised Petersen Graphs

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Abstract

We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs P(n, k) tends to zero as \(n \rightarrow \infty \). 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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Acknowledgments

The author is grateful for discussions with Sebastian Cioabă and also to the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Adrian W. Dudek

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  1. Adrian W. Dudek
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Correspondence to Adrian W. Dudek.

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Dudek, A.W. On the Spectrum of the Generalised Petersen Graphs. Graphs and Combinatorics 32, 1843–1850 (2016). https://doi.org/10.1007/s00373-016-1676-0

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  • DOI: https://doi.org/10.1007/s00373-016-1676-0

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