Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem - Rao, Yongsheng; Chen, Ruxian; Ahmad, Uzma; Ghafar Shah, Abdul (Frontiers in Physics, 2024)
Cubic fuzzy graphs offer greater utility as compared to interval-valued fuzzy graphs and fuzzy graphs due to their ability to represent the degree of membership for vertices and edges using both interval form and fuzzy numbers. The significance of these concepts motivates to analyze and interpret intricate networks, enabling more effective decision-making and optimization in various domains, including transportation, social networks, trade networks and communication systems. The paper introduces the concepts of vertex and edge connectivity in cubic fuzzy graphs, along with discussions on partial cubic fuzzy cut nodes and partial cubic fuzzy edge cuts and presents several related results with the help of some examples to enhance understanding. In addition, the paper introduces the idea of partial cubic α-strong and partial cubic δ-weak edges. An example is discussed to illustrate the motivation behind partial cubic α-strong edges. Moreover, it delves into the introduction of generalized vertex and edge connectivity in cubic fuzzy graphs, along with generalized partial cubic fuzzy cut nodes and generalized partial cubic fuzzy edge cuts. Relevant results pertaining to these concepts are also discussed. As an application, the concept of generalized partial cubic fuzzy edge cuts is employed to identify regions that are most affected by trade deficit resulting from street crimes. Finally, the research findings are compared with the existing method to demonstrate their suitability and creativity.