Mathematical analysis reveals the higher-order traces and characteristic polynomials of 5-length uniform hypercycles, highlighting spectral connections to signed graphs.
Let [Formula: see text] be a cycle with length five. The [Formula: see text]-uniform hypercycle with length five is obtained by adding [Formula: see text] new vertices in every edge of [Formula: see text], denoted by [Formula: see text]. In this paper, by using the BEST theorem and the Matrix-tree theorem, we derive the higher-order traces of [Formula: see text]. Moreover, by the relationship between the eigenvalues of power hypergraphs and signed graphs, we give the characteristic polynomials of [Formula: see text].
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Duan et al. (2026) studied this question.
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