Graph Entropy of Some Special Chemical Graphs

Chemical graph theory plays an important role in modelling molecules, especially examining physicochemical properties of the chemical compounds. Alkanes are one of the chemical compounds which are made up of hydrogen and carbon atoms, generally known as hydrocarbons. These alkanes having empirical formula CH. Structural/constitutional isomers are the collection of chemical compounds having same empirical formula but different structural arrangements, this lead to the diversity in the physicochemical properties. Graph descriptors are the essential tools in the graph theory to study about these physico-chemical properties. Some of these graph descriptors are graph spectrum, graph energy and graph entropy which contribute significantly to understand molecular properties. Spectral parameters, like spectral radius, second largest eigenvalue, spectral gap and graph energy aid in estimating energy levels and stability of the molecule, while graph entropy, such as eigenvalue-based modulus entropy derived from the adjacency matrix, measure heterogeneity. This paper explores a specific type of alkanes and their isomers, examining their spectral parameters and graph entropy. Through comparative graph plots, the nature of these parameters are observed, which sheds light on the molecular behaviours. This study shows the importance of graph theory in quantum chemistry, particularly the spectral characteristics and structural intricacies of alkanes and their isomers, contributing to a comprehensive understanding of molecular properties and behaviour at the quantum level.