Abstract
In a (crisp) graph, set of all mutually non-adjacent vertices form an independent set. This set is more crucial in graph theory. The fuzzy graphs have broader aspects over crisp graphs in real world due to vagueness. Finding fuzzy independent sets in fuzzy graphs are one of the most needful tasks. In this paper, a new term “degree of independence” to a fuzzy graph is defined by considering the strength of edges incident to the vertices of that graph. It is noticed that several networking system such as placing mobile towers or placing facility centres of multinational companies like Amazon, Flipkart, eBay, Myntra, etc. demands to identify the nodes (towers, facility centres, etc. as the case may be) which are either not connected or weakly connected to each other to optimize the cost of services that they offer. These type of networking systems can be modelled as fuzzy graphs. Also, we have studied several graph products such as Cartesian product, tensor product, and normal product and computed their degree of independence. Here, we define (fuzzy) independent set in a new way. As per our definition, any set of vertices of a graph form an independent set with degree of independence. If the degree of independence is 1, then the set becomes conventional independent set.