Predicting enthalpy of formation of benzenoid hydrocarbons and ordering molecular trees using general multiplicative Zagreb indices.

Many existing studies show that there exists a strong relationship between structures and characteristics of molecules. Topological indices are often used in modeling the properties of chemical compounds and biological activities in theoretical chemistry. Topological indices are numerical values associated with structures of molecules in such a way that they remain constant under graph isomorphism.

Conjugated tricyclic graphs with maximum variable sum exdeg index.

The variable sum exdeg index, initially introduced by Vukicevic (2011) [20] for predicting the octanol water partition co-efficient of certain chemical compounds, is an invariant for a graph and defined as , where is the degree of vertex , is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say and . The graph with maximum variable sum exdeg index is characterized from each collection given above with perfect matching.

C¹ Positive Surface over Positive Scattered Data Sites.

The aim of this paper is to develop a local positivity preserving scheme when the data amassed from different sources is positioned at sparse points. The proposed algorithm first triangulates the irregular data using Delauny triangulation method, therewith interpolates each boundary and radial curve of the triangle by C¹ rational trigonometric cubic function. Half of the parameters in the description of the interpolant are constrained to keep up the positive shape of data while the remaining half are set free for users' requirement.