Wiener index for an intuitionistic fuzzy graph and its application in water pipeline network

The usefulness of different topological indices is inevitable in various fields such as Chemistry, Electronics, Economics and Business studies, medical and social sciences. The ``purpose of this paper is to study" Wiener index for the Intuitionistic fuzzy graphs (IFG) in some detail while keeping it in parallel with the connectivity index. Some of the other distance and degree based topological indices have been defined for an IFG. Moreover, Average Wiener index has also been defined for an IFG. At the end, an application of Wiener index and Average Wiener index has also been presented in water a pipeline network which is very integral in water supply management. (C) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.