On Extremal Connected Graphs with Respect to the Forgotten Topological Index

In the study of the structure-dependency of the total -electron from 1972, it is pointed out that it depends on the sums vV d(v) 2 and vV d(v) 3 , where d(v) is the degree of a vertex v in the underlying molecular graph G.The first sum vV d(v) 2 , which was named the first Zagreb index, is one of the most investigated graphbased topological index.The second sum vV d(v) 3 has been almost completely neglected except for its potential involvement in the study of the first Zagreb index and the zeroth-order general Randi index.This second sum was named the forgotten index or F-index in short.In this paper, we investigate some properties of the F-index with respect to some new graph transformations, which are used to characterize all extremal graphs having the maximum F-index in the set Gn,m of all connected graphs of order n and size m.