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Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs

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A Correction to this article was published on 30 January 2021

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Abstract

We give an upper bound on the largest eigenvalue of the signless Laplacian matrix of a Hamiltonian graph. This bound is applied to obtain sufficient spectral conditions for the non-existence of Hamiltonian cycles. Under certain additional assumptions we provide a polynomial time decisive spectral criterion for the Hamiltonicity of a given graph with sufficiently large minimum vertex degree.

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Acknowledgements

Research of the second and the third author is partially supported by Serbian Ministry of Education, Science and Technological Development via University of Belgrade.

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Authors and Affiliations

  1. Department of Mathematics, Kuwait University, Safat, 13060, Kuwait

    Milica Anđelić

  2. Faculty of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11 000, Belgrade, Serbia

    Tamara Koledin

  3. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000, Belgrade, Serbia

    Zoran Stanić

Authors
  1. Milica Anđelić
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  2. Tamara Koledin
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  3. Zoran Stanić
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Correspondence to Milica Anđelić.

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The original online version of this article was revised due to the author has found incorrect labelling of the number of vertices of the line graph L(G) in the proof of Theorem 2 and corrected in this version.

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Anđelić, M., Koledin, T. & Stanić, Z. Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs. Bull Braz Math Soc, New Series 52, 467–476 (2021). https://doi.org/10.1007/s00574-020-00211-y

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  • DOI: https://doi.org/10.1007/s00574-020-00211-y

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