Cubic fuzzy bridges and its application to traffic flow problem

Abstract

Fuzzy graphs are of great significance in the modeling and analysis of complex systems characterized by uncertain and imprecise information. Among various types of fuzzy graphs, cubic fuzzy graphs stand out due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. The study of connectivity in fuzzy graphs depends on understanding key concepts such as fuzzy bridges, cutnodes and trees, which are essential for analyzing and interpreting intricate networks. Mastery of these concepts enhances decision-making, optimization and analysis in diverse fields including transportation, social networks and communication systems. This paper introduces the concepts of partial cubic fuzzy bridges and partial cubic fuzzy cutnodes and presents their relevant findings. The necessary and sufficient conditions for an edge to be a partial cubic fuzzy bridge and cubic fuzzy bridge are derived. Furthermore, it introduces the notion of cubic fuzzy trees, provides illustrative examples and discusses results relevant to cubic fuzzy trees. The upper bonds for the number of partial cubic fuzzy bridges in a complete CFG is calculated. As an application, the concept of partial cubic fuzzy bridges is used to identify cities most severely affected by traffic congestion resulting from accidents.