A reduction formula for the Laplacian characteristic polynomial of a uniform hypertree

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In this paper, we give a reduction formula for the Laplacian characteristic polynomial of a uniform hypertree in terms of the matching polynomials of sub-hypergraphs of a weighted uniform hypertree. Using this reduction formula, we give the multiplicity of the zero eigenvalue of the Laplacian tensor for a uniform hypertree, which confirms a conjecture by Zheng in [Linear and Multilinear Algebra, 2024;72(7):1094–1111].