Classes of hypergraphs with sum number one

A hypergraph H is a sum hypergraph iff there are a finite S ⊆ IN and d, d ∈ IN with 1 < d ≤ d such that H is isomorphic to the hypergraph Hd,d(S) = (V, E) where V = S and E = {e ⊆ S : d ≤ |e| ≤ d ∧ ∑ v∈e v ∈ S}. For an arbitrary hypergraph H the sum number σ = σ(H) is defined to be the minimum number of isolated vertices w1, . . . , wσ 6∈ V such that H ∪ {w1, . . . , wσ} is a sum hypergraph. For graphs it is known that cycles Cn and wheels Wn have sum numbers greater than one. Generalizing these graphs we prove for the hypergraphs Cn and Wn that under a certain condition for the edge cardinalities σ(Cn) = σ(Wn) = 1 is fulfilled.