Abstract
The spectral theory of Laplacian tensor is an important tool for revealing some important properties of a hypergraph. It is meaningful to compute all Laplacian H-eigenvalues for some special k-uniform hypergraphs. For a k-uniform loose path of length three, the Laplacian H-spectrum has been studied when k is odd. However, all Laplacian H-eigenvalues of a k-uniform loose path of length three have not been found out. In this paper, we compute all Laplacian H-eigenvalues for a k-uniform loose path of length three. We show that the number of Laplacian H-eigenvalues of an odd(even)-uniform loose path with length three is 7(14). Some numerical results are given to show the efficiency of our method. Especially, the numerical results show that its Laplacian H-spectrum converges to \(\{0, 1, 1.5, 2\}\) when k goes to infinity. Finally, we show that the convergence of Laplacian H-spectrum from theoretical analysis.
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The authors would like to thank the editor and the anonymous referees for their constructive comments and suggestions which led to a significantly improved version of the paper.
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Communicated by Carlos Hoppen.
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This work was supported by the National Natural Science Foundation of China (Grant no. 11771244).
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Yue, J., Zhang, L. Computing all Laplacian H-eigenvalues for a uniform loose path of length three. Comp. Appl. Math. 39, 121 (2020). https://doi.org/10.1007/s40314-020-01149-z
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DOI: https://doi.org/10.1007/s40314-020-01149-z