Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs

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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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  • 30 January 2021

    In our original paper the incorrect labelling of the number of vertices of the line graph L(G) in the proof of Theorem 2 has led to the inequality

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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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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 (2020). https://doi.org/10.1007/s00574-020-00211-y

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Keywords

  • Signless Laplacian matrix
  • Largest eigenvalue
  • Hamiltonian graph
  • Spectral inequalities

Mathematics Subject Classification

  • 05C50
  • 05C35