Determination of journeys order based on graph’s Wiener absolute index with bipolar fuzzy information

Abstract

Due to the existence of two opposite sided opinions in bipolar fuzzy graphs, the positive and negative communication between all pair of vertices always may not be strong. So, the connectivity sustain is one of the major important part in a bipolar fuzzy network system. First, Wiener index for a bipolar fuzzy graph is introduced and explained their properties. Second, the terms Wiener absolute index is created based on the total accurate connectivity between all the pair of vertices and in the whole bipolar fuzzy graph. Third, the behavior of Wiener absolute index is visualized in several bipolar fuzzy graphs like bipolar fuzzy forest, bridge, and tree. Fourth, a comparative discussion between connectivity index and Wiener index in bipolar fuzzy graphs are established. Finally, an application of all these thought is displayed in regular journeys from the city Paris to Brest.