University of Isfahan Transactions on Combinatorics 2251-8657 13 3 2024 09 01 Approachable‎ ‎ graph (tree) and ‎Its ‎application ‎in hyper (network) 287 304 27872 10.22108/toc.2023.135511.2021 EN Mohammad Hamidi Department of Mathematics, University of Payame Noor, P.O.Box 19395-4697, Tehran, Iran. 0000-0002-8686-6942 Journal Article 2022 10 25 A hypertree is a special type of connected hypergraph that removes‎ ‎any‎, ‎its hyperedge then results in a disconnected hypergraph‎. ‎Relation between hypertrees (hypergraphs) and trees (graphs) can be 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 $\alpha$-relation) on hypertrees that makes a connection 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 $q\in \mathbb{N}‎, ‎$ we introduce the concepts of a derivable tree‎, ‎$(\alpha‎, ‎q)$-hypergraph‎, ‎and fundamental $(\alpha‎, ‎q)$-hypertree for the first time in this study and analyze the structures of derivable trees from hypertrees via given positive relation‎. ‎In the final‎, ‎we apply the notions of derivable trees‎, ‎$(\alpha‎, ‎q)$-trees in real optimization problems by modeling hypernetworks and networks based on hypertrees and trees‎, ‎respectively.‎‎‎ https://toc.ui.ac.ir/article_27872_9e11259bf1260d4ea4bbe7af9308db12.pdf