Intuitionistic fuzzy Sombor indices: A novel approach for improving the performance of vaccination centers

Intuitionistic fuzzy graphs are generalizations of fuzzy graphs, in which each vertex is assigned an ordered pair whose first coordinate gives the membership value and the second coordinate gives the non-membership value. There are many theoretical parameters to study different types of graphs and fuzzy graphs, topological indices are one of them. Sombor indices are important in explaining the topology of a graph, and were found to possess useful applicative properties. The two versions of the Sombor indices ($SO_3$ and $SO_4$)are converted into an intuitionistic fuzzy framework, and then formulas for different kinds of graphs are calculated. Our study also involves setting up a network of vaccination centers during a pandemic and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implication and benefits of employing intuitionistic fuzzy-based techniques in vaccination centers. Through a comparative analysis, we evaluate which index is more efficient.