The first Zagreb and forgotten topological indices of d-ary trees

Abstract

The first Zagreb index of a graph is equal to the sum of the square of the vertex degrees of the graph and the forgotten topological index (Findex) of a graph is defined as the sum of cubes of the vertex degrees of the graph. These parameters have applications in chemistry and drug structures. For any fixed integer $d\geq2$, the d-ary tree is a rooted tree in which each node has no more than d children. We determine the mean value of these indices in d-ary trees. Also, we obtain some useful relations and equalities related to these indices and other graphical parameters.