Automorphism Groups of Alkane Graphs

Abstract

The complete set of 618047 isomers of the alkanes with 4 to 20 carbon atoms has been created. From all isomers the automorphism groups have been calculated and evaluated in terms of size, number of asymmetric carbon atoms, and numeric properties of atom and bond orbits. The presence of a symmetric bond is related to the number of atom and bond orbits. Molecular descriptors based on automorphism data have been studied, including the known symmetry index, an entropy measure and the root of an orbit polynomial. These descriptors are closely related to the presence of symmetric substructures. The prediction performance of QSPR models for three molecular properties of alkanes and using binary substructure descriptors, is improved by adding descriptors based on automorphism data.

Fixed Point Method for Nonlinear Fractional Differential Equations with Integral Boundary Conditions on Tetramethyl-Butane Graph

“…Tetramethylbutane is a hydrocarbon; it is the most heavily branched and most compact of the many octane isomers and has a highly symmetrical structure. The presence of a symmetric bond is related to the number of atoms and bond orbits [36]. The molecule's symmetrical arrangement leads to significant steric hindrance, influencing its chemical reactivity and resulting in fewer distinct hydrogen environments in spectroscopy.…”