One-two descriptor

Abstract

In this paper, we introduce the one-two descriptor. The one-two descriptors is the sum of the vertex contributions such that each pendant vertex contributes 1, each vertex of degree two adjacent to pendant vertex contributes 2, and each vertex of degree higher than two also contributes 2. We test this descriptor on the benchmark data set of the octane isomers proposed by the International Academy of Mathematical Chemistry. We show that this descriptor is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). Linear model predictions for both these properties are better then predictions of any of the benchmark descriptors proposed by International Academy of Mathematical Chemistry. Linear model predictions of TSA are also better then predictions of any of Adriatic descriptors, while linear model predictions of CP are not as good as predictions by Adriatic descriptor called inverse sum lordeg index. We also analyze the mathematical properties of this descriptor and we find tight upper and lower bounds in the families of the trees with n vertices and the chemical trees with n vertices.