approachable‎ ‎ graph (tree) and ‎its ‎application ‎in hyper (network)

Abstract. a hypertree is a special type of connected hypergraph that removes any, its hyperedge thenresults in a disconnected hypergraph. relation between hypertrees (hypergraphs) and trees (graphs) canbe helpful to solve real problems in hypernetworks and networks and it is the main tool in this regard.the purpose of this paper is to introduce a positive relation (as α-relation) on hypertrees that makes aconnection between hypertrees and trees. this relation is dependent on some parameters such as path,length of a path, and the intersection of hyperedges. for any q ∈ n, we introduce the concepts of aderivable tree, (α, q)-hypergraph, and fundamental (α, q)-hypertree for the first time in this study andanalyze the structures of derivable trees from hypertrees via given positive relation. in the final, we apply the notions of derivable trees, (α, q)-trees in real optimization problems by modeling hypernetworks andnetworks based on hypertrees and trees, respectively.