Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph ( \(\textit{FFG}\) ). The article establishes fundamental terms such as strong \(\textit{FFG}\) , complete \(\textit{FFG}\) , regular \(\textit{FFG}\) , path, degree, total degree, homomorphism, and isomorphism of \(\textit{FFG}\) , as well as the complement of \(\textit{FFG}\) . Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of \(\textit{FFG}\) s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.
