## 1 Introduction  
The concept of fuzzy graph had been proposed by [PERSON] [1] to handle indeterminate phenomena on vertices and relation between vertices. Therefore, the vertices and edges have membership degrees to represent the indeterminacy situation. In real-world problems, the degrees of non-membership of elements in a network are needed, for example, in situations that need an answer of types \"yes\" and \"no\". To handle this problem, [PERSON] [2] proposed an intuitionistic fuzzy set (IFS) and an intuitionistic fuzzy graph (IFG). Each element in IFG has membership and non-membership degrees. Numerous studies had been conducted on intuitionistic fuzzy graphs (IFGs), including the coloring of IFGs ([3,4]), the application of wiener index for IFGs in water pipeline network [5], interval-valued intuitionistic \((S,T)\)-fuzzy graphs [6], and interval-valued intuitionistic fuzzy competition graphs [7]. Two categories of memberships are not always sufficient for making decisions. Therefore, [PERSON] [8] proposed a picture fuzzy set where each element not only had membership and non-membership degrees but also had a neutral membership degree. For instance, in an election problem, the committee must count the number of people who chose or did not choose a candidate and how many abstained (the neutral condition). Further, the concept of a picture fuzzy graph (PFG) was developed in [9], wherein the vertices and edges had membership, neutral, and non-membership degrees. Researchers recently expanded PFGs in numerous types, such as q-rung PFGs [10], balanced PFGs [11], the application of PFGs for selecting best routes in an airlines network [12], picture fuzzy soft graphs [13], complex PFGs [14], regular PFGs [15], and so on. Numerousstudies had also been conducted on the use of PFGs in practical issues such as the application of balanced PFGs [11], decision making under picture fuzzy soft graphs [13], the implementation of regular PFGs in communication networks [15], road map design using picture fuzzy multigraphs [16], the application of PFGs in social networks [17], the shortest path algorithm in picture fuzzy digraphs [18], the site selection problem using laplacian energy of PFGs [19], the application of picture fuzzy tolerance graphs [20], the genus of PFGs [21], and multiple attribute decision-making via PFGs [22]. The theory of vertex coloring and edge coloring had been generalized in various types of fuzzy graphs. Some researchers proposed various generalizations of graph coloring such as the coloring of fuzzy graphs based on strong and weak adjacencies [23], fuzzy graph coloring based on \(\delta\)-fuzzy independent vertex sets [24], the fuzzy fractional coloring of fuzzy graphs [25], the fuzzy coloring of fuzzy graphs [26], the fuzzy colouring of m-polar fuzzy graphs [27], the chromatic number and perfectness of fuzzy graphs [28], and the edge coloring of fuzzy graphs [29]. Several researchers have also proposed the coloring methods through the \(\alpha\)-cut approach and two forms of adjacencies (strong and weak) in fuzzy graphs and IFGs, as seen in [3; 4; 23; 30]. The fact that a PFG is an extension of an IFG inspired us to generalize the vertex coloring from IFGs into PFGs in 2021 [31]. We utilized the \((\alpha,\beta,\delta)\)-cut approach to color PFGs. However, the computation of PFG's coloring through the cut was complicated since we should have used various values of \((\alpha,\beta,\delta)\) when determining the cut chromatic numbers. Therefore, we need another approach for coloring the PFGs. Strong and weak adjacencies--two different forms of adjacencies--between vertices in fuzzy graphs and IFGs are crucial in decision-making issues. Hence, we generalized strong and weak adjacencies into PFGs and proposed a concept to color PFGs based on strong and weak adjacencies [32]. When we work with PFGs with many vertices and edges, we need a computational tool to identify the strong and weak adjacencies and find the chromatic number of PFGs. In this paper, we construct an algorithm to handle the problem.