Upper bounds for the forgotten topological index of graphs with given domination number

Abstract

The forgotten topological index of a graph [Formula: see text], denoted by [Formula: see text], is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the degree of the vertex [Formula: see text]. In this paper, we establish upper bounds on the forgotten topological index of trees, unicyclic graphs and bicyclic graphs with a given domination number.