Details of Research Outputs

On a basic element, vertex degree, of topological graphs, insights are obtained on the structural features hidden in the degree distributions (DD) of saturated hydrocarbons. The investigation shows that the cyclicity and branching features are mainly coded by the different mathematical characteristics of the degree distributions. Surprisingly, the center (or mathematical expectation) of a degree distribution corresponds to the cyclicity of a saturated hydrocarbon, and the dispersion (mean absolute deviation or MAD) around its center of a distribution is a measure of branching. The structural feature such as number of quaternary atoms is also mined out as a special case of branching. The cyclicity and branching information in the present work is with least human intervention, and an interesting thing is that the two features can be unified into the mathematical characteristics of a degree distribution. By the strict mathematical characteristics of a distribution, the structure features within the degree distributions (DD somer domains) are studied. The space spanned by the size (number of carbons), mathematical expectation, and MAD shows some enlightening results. The results also give a new idea on how to model the properties of diverse structures.