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

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Article Type:
Research/Original Article (دارای رتبه معتبر)
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.‎‎‎
Language:
English
Published:
Transactions on Combinatorics, Volume:13 Issue: 3, Sep 2024
Pages:
287 to 304
https://www.magiran.com/p2662557  
سامانه نویسندگان
  • Mohammad Hamidi
    Author
    Associate Professor Mathematics- Science, Payame Noor University, Tehran, Iran
    Hamidi، Mohammad
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