The characteristic polynomials of uniform double hyperstars and uniform hypertriangles

Abstract

A k-power hypergraph is obtained from a graph by adding k−2 new vertices to each edge of the graph. A k-uniform double hyperstar is the k-power hypergraph of a double star. The k-uniform hypertriangle is the k-power hypergraph of a triangle. We present the characteristic polynomials of uniform double hyperstars by using the Poisson formula. Moreover, we find expressions for the traces of uniform hypertriangles and use these to obtain the characteristic polynomials of uniform hypertriangles.