Fuzzy Graph Structures and Its Properties

Objectives: To find the vertex cohesive number and edge cohesive number of Gear and Bistarfuzzy graph structure. Methods/ Statistical Analysis: Gear graph and Bistar graph is converted into a fuzzy graph by assigning membership function for vertices and edges. The edges with same membership function are grouped to get a gear and Bistar fuzzy graph structure. For this Gear and Bistar fuzzy graph structure, vertex and edge cohesive number are computed. Findings: The vertex and edge cohesive number of Gear and Bistar fuzzy graph structure are found. Application: In any organisation, the employees can be treated as vertices. Keeping in mind how one employee co-ordinates with other employee, one can study how employees can work in groups.