Some operations on intuitionistic fuzzy graphs via novel versions of the Sombor index for internet routing

Abstract

AbstractTopological indices (TIs) are numerical structures that are associated with a graph to identify its topology. TIs are highly popular in the literature with a wide range of applications from chemistry to economics. However, TIs have limitations in representating complex relations within the graphs creating some uncertainities. Fuzzy graph (FG) and intuitionistic fuzzy graph (IFG) are introduced to overcome these uncertainities. While a FG a describes degree of membership of an object in a graph, IFG delineate information on membership or nonmembership under uncertainity. This study aims to introduce novel TIs such as the general second Zagreb index, the Sombor index of the third version, and the Sombor index of the fourth version in the IFG framework in order to improve practicality of FG and IFG applications. Some properties of the proposed indices and their upper bounds are provided as well. Proposed TIs are applied to an internet routing network as a case study. Results of the study show that adding more internet routers in the network can increase internet speed and the strength of the entire system. Finally, comparative studies for the Sombor index of the third version and the Sombor index of the fourth version are also revealed.