Edge integrity for signed fuzzy graphs

Transport network is the backbone of economy. Every path has some positive and negative attributes such as transportation cost, road condition, traveling time etc., These attribute values are taken as fuzzy membership value with either positive or negative sign when modeling the transport network as signed fuzzy graph. The stability of these type of signed fuzzy graphs are discussed with the help of vulnerability parameters and edge integrity. In this paper, we have introduced complete signed fuzzy graph, signed fuzzy star graph, complement of a signed fuzzy graph, union of two signed fuzzy graph, join of two signed fuzzy graph and cartesian product of two signed fuzzy graphs. For some standard signed fuzzy graph edge integrity value is calculated. Further this concept is applied in supply chain network with three layers, to study its stability and optimum path.