  Topological indices have important role in theoretical chemistry for QSPR
researches. Among the all topological indices the Randi\'c and the Zagreb
indices have been used more considerably than any other topological indices in
chemical and mathematical literature. Most of the topological indices as in the
Randi\'c and the Zagreb indices 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 we define ev-degree Zagreb
index, ve-degree Zagreb indices and ve-degree Randi\'c index by using these new
graph invariants as parallel to their corresponding classical degree versions.
We compare these new group ev-degree and ve-degree indices with the other
well-known and most used topological indices in literature such as; Wiener,
Zagreb and Randi\'c indices by modelling some physicochemical properties of
octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb
and the ve-degree Randi\'c indices give better correlation than Wiener, Zagreb
and Randi\'c indices to predict the some specific physicochemical properties of
octanes. We investigate the relations between the second Zagreb index and
ev-degree and ve-degree Zagreb indices and some mathematical properties of
ev-degree and ve-degree Zagreb indices. Keywords:
