Entire forgotten topological index of graphs

Abstract

The Forgotten topological index or F-index is defined as the sum of cubes of the degrees of vertices of a graph. For this classical F-index, we ignore the intermolecular forces that exist between the atoms and bonds and consider only the intermolecular forces between the atoms of a molecule. In this paper, we introduce a new graph invariant called "Entire Forgotten topological index" or "Entire F-index': that includes incidency of edges and vertices in addition to the adjacency of the vertices. We obtain some important properties of the index and also establish formulae of this newly defined index for some operations of graphs.