Planarity in cubic intuitionistic graphs and their application to control air traffic on a runway

Fuzzy modeling plays a pivotal role in various fields, including science, engineering, and medicine. In comparison to conventional models, fuzzy models offer enhanced accuracy, adaptability, and resemblance to real-world systems and help researchers to always make the best choice in complex problems. A type of fuzzy graph that is widely used in medical and psychological sciences is the cubic intuitionistic fuzzy graph, which plays an important role in various fields such as computer science, psychology, medicine, and political sciences. It is also used to find effective people in an organization or social institution. In this research endeavor, we embark upon elucidating the innovative notion of a cubic intuitionistic planar graph, delving into its intricate properties and attributes. Additionally, we unveil the novel concept of a cubic intuitionistic dual graph, thus enriching the realm of graph theory with further profundity. Furthermore, our exploration encompasses the elucidation of other pertinent terminologies, such as cubic intuitionistic multi-graphs, along with the categorization of edges into the distinct classifications of strong and weak edges. Moreover, we discern the concept of the degree of planarity within the context of CIPG and unveil the notion of strong and weak faces. Additionally, we delve into the construction of cubic intuitionistic dual graphs, which can be realized in cases where the initial graph is planar or possesses a degree of planarity & GE;0.67. Notably, we furnish the exposition with a comprehensive discussion on noteworthy findings and substantial results pertaining to these captivating topics, contributing valuable insights on the field of graph theory. Last, we shall endeavor to exemplify the practical relevance and importance of our research by presenting an illuminating real-world application, thus demonstrating the tangible impact and significance of our endeavors in this research article.