Exact Formulae for Degree Distance Indices of Sum Graphs

Abstract

The degree distance index (DDI) is a vertex-degree weighted version of a well-known index that is called by Wiener index (WI). In extremal theory of graphs, improving the bounds with best possible values is a worth investigating problem. In this note, the exact formulae of the $\mathrm{DDI}$ for the four different types of the sum graphs in the terms of various indices of their factor graphs are computed. Moreover, a comparison is also presented between the obtained exact and already existing bounded values for the particular sum graphs.