H-Restrainedness for Hypergraphs

Abstract

I introduce a new concept for hypergraphs called H-restrainedness. I prove that an H-restrained set of a hypergraph does not contain a vertex of minimality if and only if the compliment of S is an Hdominating set. I also prove a necessary and sufficient condition under which the restrainedness number of a hypergraph decreases when a vertex is removed from the hypergraph. I have proven that Let G be a hypergraph and ???? ⊆ ????(????) be an H-restrained set of G then S is 1-minimal if and only if every vertex of S is an H-enclave point of S then I have given the examples when a G be a hypergraph and ???? ∈ ????(????) then ????????ℎ(????\{????}) < ????????ℎ(????) ⇔ there is a reh set S with at least two vertices of G containing v.