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This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.

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This paper considers wireless sensor (hyper) networks by single-valued neutrosophic (hyper)graphs. It tries to extend the notion of single-valued neutrosophic graphs to single-valued neutrosophic hypergraphs and it is derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via positive equivalence relation. We use single-valued neutrosophic hypergraphs and positive equivalence relation to create the sensor clusters and access to cluster heads. Finally, the concept of (extended) derivable single-valued neutrosophic graph is considered as the energy clustering of wireless sensor networks and is applied this concept as a tool in wireless sensor (hyper) networks.

The purpose of this paper is to introduce the notation of single-valued neutrosophic hyper BCK-subalgebras and a novel concept of neutro hyper BCK-algebras as a generalization and alternative of hyper BCK-algebras, that have a larger applicable field. In order to realize the article’s goals, we construct single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras on a given nonempty set. The result of the research is the generalization of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras to single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras, respectively. Also, some results are obtained between extended (extendable) single-valued neutrosophic BCK-subalgebras and single-valued neutrosophic hyper BCK-subalgebras via fundamental relation. The paper includes implications for the development of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras and for modelling the uncertainty problems by single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras. The new conception of single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras was given for the first time in this paper. We find a method that can apply these concepts in some complex networks.