Y-coindex of graph operations and its applications of molecular descriptors

Abstract

The methods on topological index and topological coindex computation are very suitable and serviceable for developing countries in which they can yield available medical information about new drugs without chemical experiment. For example, in quantitative structure-activity relationships (QSAR) modelling, the predictors consist of theoretical molecular descriptors of chemicals, while the (QSAR) response-variable could be a biological, pharmacological, medical, ecological activity of the chemicals. Recently, proposed new invariant of this kind is the Y-index defined as: Y (G)=? u? V (G) ? G 4 (u)=? u v? E (G)[? G 3 (u)+ ? G 3 (v)], In this paper, the basic relations between this index and its coindex for a graph G and its complement G� are determined. We compare this new coindex with the other well-known and most used topological indices and coindices in literature by modelling some physicochemical properties of octane isomers. We will find that, the Y-coindex give better correlation than others. Also, we explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.