STUDY OF COHESIVE NUMBER IN HESITANT FUZZY GRAPHS
By
Nikita Prajapati and Gautam Patel
Department of Mathematics, Gandhinagar University, Gandhinagar, Gujarat, India-395007
Email: nikitakp2110@gmail.com, gautamvpatel26@gmail.com (Received: August 19, 2025; In format: September 06, 2025;
Revised: October 30, 2025; Accepted: November 01, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55206
Abstract
This study aims to determine the vertex cohesive number and edge cohesive number of hesitant fuzzy graph structures derived from Gear and Bipartite graphs. The Gear and Bipartite graphs are transformed into hesitant fuzzy graphs by assigning hesitant fuzzy membership functions to both vertices and edges. Similar hesitant fuzzy membership functions are grouped to form cohesive hesitant fuzzy structures. The vertex and edge cohesive numbers for these structures are then computed. These findings provide insights into the cohesiveness of vertices and edges within hesitant fuzzy graphs. The approach can be applied in organizational contexts, where employees are modeled as vertices. By analyzing the coordination between employees using hesitant fuzzy graph structures, it becomes possible to gain valuable insights into group dynamics and improve team efficiency. This study utilizes vertex and edge cohesive numbers in hesitant fuzzy graphs to optimize transportation networks under uncertain conditions.
2020 Mathematical Sciences Classification: 05C72.
Keywords and Phrases: Hesitant Fuzzy Vertex and Edge, Vertex and Edge Cohesive Number, Hesitant Fuzzy Gear Graph, Hesitant Fuzzy Bipartite Graph.