Affiliations: [a]
Department of Mathematics, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu, India
| [b]
Department of Mathematics, SSN College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu, India
| [c]
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
Correspondence:
[*]
Corresponding author. Sankar Sahoo, Department of Applied Mathematics with Oceanology and Computer Programming,
Vidyasagar University, Midnapore, India. E-mail: [email protected].
Abstract: The stability of a network is measured by vulnerability parameters. Integrity is one the most important vulnerability parameter in the field of graph network. An uncertain network can be modeled as a fuzzy graph. In this paper, vertex integrity of fuzzy graph is introduced and illustrated with example. Also, we introduced the vertex integrity of the union, join and Cartesian product of two fuzzy graphs and established many interesting results on them. Finally, we discussed edge integrity of fuzzy graph with suitable illustration and investigated many results on edge integrity of fuzzy graph.
Keywords: Vertex integrity, edge integrity, join of fuzzy graph, cartesian product of fuzzy graph, union of fuzzy graph
