Approachable‎ ‎ graph (tree) and ‎Its ‎application ‎in hyper (network)

Hamidi, Mohammad

doi:10.22108/toc.2023.135511.2021

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	Approachable‎ ‎ graph (tree) and ‎Its ‎application ‎in hyper (network)
Transactions on Combinatorics
دوره 13، شماره 3، آذر 2024، صفحه 287-304 اصل مقاله (560.21 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2023.135511.2021
نویسنده
Mohammad Hamidi^*
Department of Mathematics, University of Payame Noor, P.O.Box 19395-4697, Tehran, Iran.
چکیده
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.‎‎‎
کلیدواژه‌ها
‎$\alpha$-Relation؛ Fundamental $(\alpha؛ q)$-hypergraph؛ $k$-Parts

مراجع
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Approachable‎ ‎ graph (tree) and ‎Its ‎application ‎in hyper (network)