Let T ∆ n denote the set of trees of order n, in which the degree of each vertex is bounded by some integer ∆. Suppose that every tree in T ∆ n is equally likely. We show that the number of vertices of degree j in T ∆ n is asymptotically normal with mean (μj + o(1))n and variance (σj + o(1))n, where μj , σj are some constants. As a consequence, we give estimate to the value of the general Zagre...

A QSPR (quantitative structure-property relationship) model for the estimation of the liquid viscosity of a large variety of organic compounds was established using the CODESSA (comprehensive descriptors for structural and statistical analysis) approach. The final model was developed with a calibration set containing 337 compounds. The multilinear regression (MLR) equation that relates ln η to ...

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

We give a proof of the index theorem lattice Wilson–Dirac operators, which states that twisted Dirac operator on standard torus is described in terms corresponding operator. Our based higher theory almost flat vector bundles.