On the Terminal Wiener Index of Networks

Finding quantitative measures for describing and social characterizing the structural properties of networks is a research topic with ongoing interest. These measures are called graph invariants and are usually referred to as topological indices. The oldest topological index is the Wiener index, it has been extensively studied in many applications such as chemical graph theory, complex network, social networks, and computer net-works. After the success of the Wiener index, a large number of modifications and extensions of the Wiener index have been proposed in the literature. In this paper, we focus our attention to the most recent topological index, called the Terminal Wiener index. Then, we are going to present the structure of networks that attain the second maximal Terminal Wiener index, and we propose a network transformation that increases the Terminal Wiener index.