Affiliations: [a] Department of Mathematics, R V Institute of Technology and Management, JP Nagar, Bangalore, India
| [b] Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India
Correspondence:
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Corresponding author. Sivasankar S., Department of Mathematics, R V Institute of Technology and Management, JP Nagar, Bangalore-560076, India. E-mail: [email protected].
Abstract: A new concept of vertices in a fuzzy graph known as defective vertices is introduced here. A vertex in a fuzzy network is called defective if no edges incident with it are strong. Defective vertex cannot be ignored when determining dominance in a fuzzy network because they are a part of the network. Finding defective vertices in a network is not much difficult when the adjacency matrix is given. In this paper, the novel concept of defective vertices of a fuzzy graph is introduced. Based on this idea a stable domination set and a stable domination number are defined. This also optimised the network by establishing minimal connectivity. We have proposed three algorithms for finding the defective vertices, establishing stable connectivity, and determining the stable domination number for a given graph. An application of stable domination in the diagnosis of chickenpox disease is demonstrated to show the effectiveness of the proposed algorithms.
