A molecular graph is a representation of the structural formula of a chemical compound in terms of graph theory, whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds between atoms. In chemical graph theory, an interesting emerging subfield called cheminformatics deals with a chemical phenomenon known as quantitative structure activity and structure-property relationships of chemical compounds. The methods of cheminformatics are also used for the prediction of properties relevant to the drug discovery and optimization process. For example, knowledge discovery can be used for the identification of lead compounds in pharmaceutical data matching. An emerging tool, used in the study of these phenomena, is a topological index which remains constant for all chemical structures up to their symmetries. In 1947, Harry Wiener introduced a topological descriptor known as the Wiener index that later became one of the most useful and popular molecular descriptors. Wiener applied this index to determine the physical properties of certain types of alkenes known as paraffin. Its fascination came from the mathematical simplicity in attributing numbers to chemical structures by counting of vertices, neighbors, and reciprocal relationships. The study of topological indices on the chemical structure of drugs can provide a theoretical basis for the manufacturing of drugs and chemical materials. A number of topological indices are determined in view of edge dividing methods which provide a remedy to the lack of medicinal experiments.

Molecular topological indices are now a subject of important multidisciplinary research because of their immense number of applications in various branches of applied sciences. In this era of rapid technological development, chemical and pharmaceutical techniques in recent years have rapidly evolved, and thus a large number of new nanomaterials, crystalline materials, and drugs emerge every year. Determining the chemical properties of such a large number of new compounds and new drugs requires a large number of chemical experiments, thereby greatly increasing the workload of chemical and pharmaceutical researchers. Fortunately, chemical-based experiments have found a strong connection between the topology of molecular structures and their physical behaviors, chemical characteristics, and biological features, such as melting point, boiling point, and toxicity of drugs.

The aim of this Special Issue is to attract leading scientists, chemists, and researchers working in this interdisciplinary area in order to contribute new methods, techniques, and computing algorithms on various theoretical and computational aspects of these indices. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Molecular topological indices
• Chemical graph theory and applications
• Topological indices and quantitative structure–property relationship (QSPR) analysis of drugs
• Graph optimization problems for topological indices
• Counting related indices and polynomials on topological indices
• Entropy of molecular graphs
• Irregularity indices of graphs
• Topological indices of nanostructures
• Algorithms and computational issues for topological indices