Certain indices of graphs under bipolar fuzzy environment with applications

Connectivity index of graph plays a significant role in chemistry, pharmacology, etc. This paper brings in connectivity index of a bipolar fuzzy graph (BFG) with its boundedness. We examine the changes of connectivity index for a BFG when a vertex or an edge is removed. Some theorems related to these are established. The parameter, average connectivity index of a BFG, is introduced with some theorems. Some special types of nodes like bipolar fuzzy connectivity-enhancing node, bipolar fuzzy connectivity-reducing node, bipolar fuzzy connectivity-neutral node with their properties are introduced. Keeping in mind bipolar judgemental thinking, two applications of these thoughts are bestowed to increase the popularity of women football league in India and another is to determine the order of the places to build colleges in a town.