Connectivity status of fuzzy graphs

Network science is a widely studied subject and graph theory has a major role in it. This paper studies connectivity status of vertices in a fuzzy graph. This paper adopt connectivity status to build up the status sequence related to a fuzzy graph. Results on connectivity status and status sequence of different structures are obtained. On the basis of connectivity status, vertices of a fuzzy graph can be classified into connectivity status enhancing vertices, connectivity status reducing vertices and connectivity status neutral vertices. Connectivity status analysis of vertices is also carried out. Algorithms related to these concepts are provided and an application related to bandwidth allocation problem in networking is proposed.