## 4 Main Results
### An Algorithm for Finding the Chromatic Number of PFGs
Furthermore, we constructed an algorithm (Algorithm 1) for determining the chromatic number of PFGs and implement it in Python and Matlab R2022b to assess the algorithm's performance. The correctness of Algorithm 1 was also proved using mathematical induction. Additionally, we improved the method to model traffic flows at an intersection using PFGs and to determine an intersection's traffic light phasing. We took a case study at an intersection in the Special Region of Yogyakarta-Indonesia to evaluate the method. The outcome demonstrated that there were no concurrent traffic flows from merging conflict that moved at the same phase. The traffic signal phasing acquired using the PFG coloring method was found to be safer than the signal phasing obtained using the fuzzy graph coloring method. Further research can be carried out to improve the method for handling traffic signal phasing at any intersection, such as implementing the method for the five way-intersection and integrating the algorithm with automatic counting for traffic flow data at the intersection. In the basic theories of PFG's coloring, we can investigate the chromatic number of certain operations of two PFGs, such as union, join, Cartesian product, and composition of two PFGs. Conceptualization, I.R. ; methodology, I.R. ; software, I.R. ; validation, I.R. and C.R.I. ; formal analysis, I.R. and C.R.I. ; investigation, I.R. ; resources, I.R. ; data curation, I.R. ; writing--original draft preparation, I.R. ; writing--review and editing, C.R.I. ; visualization, I.R. ; supervision, C.R.I. ; project administration, C.R.I. ; and funding acquisition, C.R.I. All authors have read and agreed to the published version of the manuscript. This research was funded by the postdoctoral program Universitas Gadjah Mada under grant number 6468/UN1/DITLIT/Dit-Lit/PT.00/2022. Data Availability Statement: Data are contained within the article. The authors express their gratitude to the reviewers for their insightful feedback on how to make the work better. The authors declare no conflict of interest. Figure 11: The fuzzy graph model of traffic flows in the Pingit intersection. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l}
**IFS** & Intuitionistic fuzzy set \\
**IFG** & Intuitionistic fuzzy graph \\
**PFS** & Picture fuzzy set \\
**PF** & Picture fuzzy \\
**PFVS** & Picture fuzzy vertex set \\
**PFES** & Picture fuzzy edge set \\
**PFG** & Picture fuzzy graph \\
**NeuM** & Neutral membership \\
**CPFG** & Complete picture fuzzy graph \\ \end{tabular} 

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