On the f-Index of Some Special Graphs

Articles on the topological indices based on the distance between any two vertices on the graph have been intensively increasing recently, as there are several distance formulas in graph theory depending on what researchers have put. The ordinary distance d(u,v) is the length of the shortest path between vertices u and v in a connected graph. In this paper, the new distance defined on a connected graph is f-distance based on the ordinary distance. This research includes giving several characteristics related to f-distance after providing a definition of f-distance, in addition to finding f-index and average f-distance for some private graphs.