Abstract
In the realm of handling imprecise information, picture fuzzy cubic sets have emerged as a more versatile tool compared to cubic sets, cubic intuitionistic fuzzy sets, and similar models. These sets offer better adaptability, precision and compatibility with the system than existing fuzzy models. This paper extends the concept of picture fuzzy cubic sets to the domain of graph theory, introducing the novel concept of picture fuzzy cubic graphs that surpasses previous results in terms of generality. The paper explores various essential operations, including composition, the Cartesian product, P-join, R-join, P-union, R-union of picture fuzzy cubic graphs. It also investigates the order and degree of picture fuzzy cubic graphs. Furthermore, this work presents two practical applications of picture fuzzy cubic graphs. The first application involves computing the impact of other companies on a specific company and the second application focuses on evaluating the overall impact within a group of companies.
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