Classes of hypergraphs with sum number one

A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ with 1 < d̲ < d̅ such that ℋ is isomorphic to the hypergraph ${\displaystyle {\mathscr{H}}_{d̲,d̅}\left(S\right)=(V,)}$ where V = S and ${\displaystyle =\{e\subseteq S:d̲<\left|e\right|<d̅\wedge {\sum }_{v\in e}v\in S\}}$. For an arbitrary hypergraph ℋ the sum number(ℋ ) is defined to be the minimum number of isolatedvertices ${\displaystyle w₁,...,w_{\sigma }\notin V}$ such that ${\displaystyle \mathscr{H}\cup \{w₁,...,w_{\sigma }\}}$ is a sum hypergraph. For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs ₙ and ₙ that under a certain condition for the edgecardinalities (ₙ)= (ₙ)=1