The Characteristic Polynomials of Uniform Hypercycles with Length Five

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].