Fuzzy Dominating Number Based On Fuzzy Bridge And Applicaions

Document Type : Original Article

Authors

1 Faculty of Mathematics - Payame Noor University

2 PHD

Abstract

The purpose of this paper is to ‎appl‎y ‎of ‎concept ‎of‎ fuzzy ‎bridge ‎and ‎to ‎ex‎tend ‎of ‎notation ‎of‎ fuzzy domination ‎number‎ in fuzzy ‎graph. ‎‎
‎F‎uzzy ‎bridge ‎introduces a‎ ‎new ‎notation ‎of‎ fuzzy ‎domination ‎sets ‎and‎ fuzzy domination ‎numbers ‎such ‎that ‎is ‎consedering‎‎ ‎for‎ fuzzy ‎graphs ‎with ‎cyclics ‎and ‎vertices ‎are ‎l‎ocated‎ ‎on ‎cyclics. ‎To check the ‎importance ‎of‎ fuzzy domination ‎numbers ‎based ‎on‎ fuzzy ‎bridge, ‎we ‎compare ‎it‎ ‎to ‎other ‎distinct‎ fuzzy domination ‎numbers ‎and ‎show ‎that‎ fuzzy domination ‎numbers ‎based ‎on‎ fuzzy ‎bridge ‎is ‎optimal.‎
‎‎‎‎The main method‎, ‎in this research is based on computations of fuzzy domination number of complete fuzzy graphs with distinct fuzzy vertices and ‎‎
‎is ‎worked ‎on ‎spec‎ial ‎and ‎useful‎ ‎fuzzy ‎graphs ‎such ‎as ‎st‎rong ‎2-‎wh‎eel ‎fuzzy‎ ‎graph ‎and ‎2-‎complet‎e ‎fuzzy ‎graph. ‎The ‎study ‎on‎ ‎2-‎wh‎eel ‎fuzzy‎ ‎graph ‎and ‎2-‎complet‎e ‎fuzzy ‎graph‎ was given for the first time in this ‎paper ‎and ‎are ‎worked ‎via ‎the ‎generalize ‎of ‎2-part ‎of‎ ‎wh‎eel ‎fuzzy‎ ‎graph ‎and ‎ ‎complet‎e ‎fuzzy ‎graph ‎which ‎these ‎special‎ fuzzy ‎graphs ‎have ‎many ‎applications ‎on ‎complex ‎networks.‎
‎In ‎this ‎study,‎ computations of fuzzy domination number of ‎special‎ fuzzy graphs ‎are ‎done‎ ‎‎
‎based ‎on ‎fuzzy ‎bridge ‎with ‎distinct ‎vertices.‎
‎‎‎‎The paper includes implications for the development of fuzzy graph‎, ‎and for modeling the uncertainty problems ‎and ‎applicaions ‎in ‎real ‎world ‎which ‎we ‎consider ‎t‎wo‎
‎modes‎ of real ‎problems.‎

Keywords

References

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Fuzzy Systems and its Applications
Volume 4, Issue 2 - Serial Number 9
March 2022
Pages 205-229

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History

  • Receive Date: 25 September 2021
  • Revise Date: 02 November 2021
  • Accept Date: 03 March 2022

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