The Characteristic Polynomials of Uniform Double Starlike Hypertrees and Uniform Squids

Abstract

A [Formula: see text]-power hypergraph is obtained from a graph by adding [Formula: see text] new vertices to each edge of the graph. Let [Formula: see text] be a graph obtained by adding [Formula: see text] edges and [Formula: see text] edges to the two pendant vertices of a path of length 2, respectively. A [Formula: see text]-uniform double starlike hypertree is the [Formula: see text]-power hypergraph of [Formula: see text], denoted by [Formula: see text]. A [Formula: see text]-uniform squid is obtained by adding [Formula: see text] pendant edges to [Formula: see text] vertices on a single hyperedge with [Formula: see text] vertices. In this paper, we give the characteristic polynomials of uniform double starlike hypertrees and uniform squids using the Poisson formula.