The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and fuzzy graph structures, shows better capabilities in solving complex problems, especially in cases where there are multiple relationships. The quality and method of determining the degree of vertices in this type of fuzzy graphs simultaneously supports fuzzy membership and interval-valued fuzzy membership, in addition to the multiplicity of relations, motivated us to conduct a study on the maximal product of cubic fuzzy graph structures. In this research, upon introducing the cubic fuzzy graph structure, some properties of the maximal product and its characteristics have been investigated. By introducing the degree and the total degree of a vertex in the product of at most two cubic fuzzy graph structures, its calculation methods are categorized based on different conditions among the membership functions of vertices and edges. The results show that all features of two cubic fuzzy graph structures do not appear in their maximal product and vice versa. Finally, an application of cubic fuzzy graph structure in project management is presented.
