A New Tool for QSPR Researches: ev-degree Randić Index

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randic index has been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randic index are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study ev-degree Randic index is defined by using ev-degree concept as parallel to their corresponding classical degree version. This new ev-degree Randic index is compared with the Randic index by modelling some physicochemical properties of octane isomers. It is showed that the ev-degree Randic index give better correlation than the Randic index to predict the entropy, acentric factor and  standard enthalpy of vaporization of octanes.  Also the exact values of the ev-degree Randic index for the well-known graph classes such as; paths, cycles, stars and complete graphs are given.