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

Document Type : Research Paper

Author

Department of Mathematics, University of Payame Noor, P.O.Box 19395-4697, Tehran, Iran.

Abstract

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.‎‎‎

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References

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Transactions on Combinatorics
Volume 13, Issue 3 - Serial Number 3
September 2024
Pages 287-304

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History

  • Receive Date: 25 October 2022
  • Revise Date: 16 June 2023
  • Accept Date: 01 October 2023
  • Published Online: 01 September 2024

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