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The formula for the spectral moment of graphs which is represented by the number of subgraphs is called the RNS spectral moment formula of graphs. In this paper, the research on the RNS spectral moment formula of graphs is generalized to hypergraphs. We give a formula for the spectral moment of a hypertree in terms of the number of some subhypertrees. Using this formula, we obtain the first 3 k  codegree coefficients of the characteristic polynomial of a  k -uniform hypertree in terms of the number of some subhypertrees.

Spectral moments of hypertrees and their applications