Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

Sankar Das, Ganesh Ghorai, Qin Xin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
13 Downloads (Pure)


In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources.
Original languageEnglish
Number of pages17
Issue number5
Publication statusPublished - 7 May 2022


  • picture fuzzy graph
  • picture fuzzy threshold graph
  • picture fuzzy split graph
  • picture fuzzy threshold dimension
  • picture fuzzy partition number


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