New upper bounds for the forgotten index among bicyclic graphs

Abstract

The forgotten topological index of a graph G, denoted by F (G), is defined as the sum of weights d(u) 2 + d(v) 2 over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper, we give sharp upper bounds of the F-index (forgotten topological index) over bicyclic graphs, in terms of the order and maximum degree.