Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

Connectivity and strength has a major role in the field of network connecting with real world life. Complexity function is one of these parameter which has manifold number of applications in molecular chemistry and the theory of network. Firstly, this paper introduces the thought of complexity function of fuzzy graph with its properties. Second, based on the highest and lowest load on a network system, the boundaries of complexity function of different types of fuzzy graphs are established. Third, the behavior of complexity function in fuzzy cycle, fuzzy tree and complete fuzzy graph are discussed with their properties. Fourth, applications of these thoughts are bestowed to identify the most effected COVID-19 cycles between some communicated countries using the concept of complexity function of fuzzy graph. Also the selection of the busiest network stations and connected internet paths can be done using the same concept in a graphical wireless network system.