The Degree-distance of the Newkome-type Trees

Abstract

The Newkome resinol is a kind of synthetic macromolecule compounds which could be described by a graph with 253 vertices and 36 leaves. Based on the structure of Newkome resinol, a kind of trees (called the Newkome-type tree) is defined in this paper. According to the recursive structure of the Newkome-type trees, the vertex-degree-distance and the degree-distance of the graph are studied, and the analytic expression of the vertex-degree-distance of all vertices and the degree-distance of the graph are obtained.