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Finding all H-Eigenvalues of Signless Laplacian Tensor for a Uniform Loose Path of Length Three

Author

Listed:
  • Junjie Yue

    (Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China)

  • Liping Zhang

    (Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China)

Abstract

H-spectra of adjacency tensor, Laplacian tensor, and signless Laplacian tensor are important tools for revealing good geometric structures of the corresponding hypergraph. It is meaningful to compute H-spectra for some special k-uniform hypergraphs. For an odd-uniform loose path of length three, the Laplacian H-spectrum has been studied. In this paper, we compute all signless Laplacian H-eigenvalues for the class of loose paths. We show that the number of H-spectrum of signless Laplacian tensor for an odd(even)-uniform loose path with length three is 7(13). Some numerical results are given to show the efficiency of our method. Especially, the numerical results show that the H-spectrum is convergent when k goes to infinity. Finally, we present a conjecture that the signless Laplacian H-spectrum converges to {1, 1.5, 2} ({0, 1, 1.5, 2}) for odd (even)-uniform loose path of length three.

Suggested Citation

  • Junjie Yue & Liping Zhang, 2020. "Finding all H-Eigenvalues of Signless Laplacian Tensor for a Uniform Loose Path of Length Three," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-13, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400072
    DOI: 10.1142/S0217595920400072
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