chapter  Chapter 32
7 Pages

Q-Wiener Index

WithAsma Hamzeh, Ali Iranmanesh

The Wiener index is the sum of distances between all pairs of vertices of a connected graph. q-Analogs find applications in a number of areas, including the study of fractals and multifractal measures, and expressions for the entropy of chaotic dynamical systems. q-Analogs also appear in the study of quantum groups and in q-deformed superalgebras. q-Analogs of the Wiener index, motivated by the theory of hypergeometric series. Usage of topological indices in chemistry began in 1947 when chemist Harold Wiener developed the most widely known topological descriptor, the Wiener index, and used it to determine physical properties of types of alkanes known as paraffin. q-Analogs find applications in a number of areas, including the study of fractals and multi-fractal measures, and expressions for the entropy of chaotic dynamic systems. q-Analogs also appear in the study of quantum groups and in q-deformed superalgebras.