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

摘要

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.