The Characteristic Polynomial of a Uniform Hypercycle

Abstract

It is (and was) an increasingly significant field of study to analyze the graph properties using the spectra of the various
matrices associated with the graph. The computation of the characteristic polynomial (either explicitly or recursively)
of the hypermatrices associated with the uniform hypergraphs is really a challenging and interesting task. In this article,
we obtain all the coefficients of the characteristic polynomial of the degree-based extended adjacency hypermatrices
associated with an r-uniform hypercycle of arbitrary length.