Theoretical chemistry is the branch of chemistry in which chemists develop theoretical generalizations that are part of the theoretical arsenal of modern chemistry. Chemical graph theory plays an important role in theoretical chemistry. Mathematical chemistry has recently presented a wide range of ways to deal with understanding the chemical structures which underlie existing chemical ideas, creating and researching novel mathematical models of chemical phenomena, and utilizing mathematical concepts and procedures in chemistry. Since the seminal paper of the American chemist Harold Wiener in 1947, many numerical quantities of graphs have been introduced and extensively studied to describe various physicochemical properties. Such graph invariants are most referred to as topological indices and are often defined using degrees of vertices, distances between vertices, eigenvalues, symmetries, and many other properties of chemical structures. The structure of a chemical compound is frequently viewed as a set of functional groups arrayed on a substructure. From a graph-theoretic perspective, the structure is a labelled graph where the vertex and edge labels specify the atom and bond types, respectively. From this perspective, the functional groups and substructure are simply subgraphs of the labelled graph representation. By changing the set of functional groups and/or permuting their positions, a collection of compounds is essentially defined that are characterized by the substructure common to them. Traditionally, these positions simply reflect uniquely defined atoms (vertices) of the substructure (common subgraph). These positions seldom form a minimum set that is known as resolving set. Under the traditional view, we can determine whether any two compounds in the collection share the same functional group at a position. This comparative statement plays a critical role in drug discovery whenever it is to be determined whether the features of a compound are responsible for its pharmacological activity.

There are well-studied groups of molecules composed of carbon and hydrogen atoms but modelling of more complex heteroatomic compounds is much more challenging. On the other hand, topological indices have also found enormous applications in rapidly growing research of complex networks, which include communications networks, social networks, biological networks, etc. In such networks, these indices are used as measures for various structural properties.

The purpose of this Special Issue is to report and review recent developments concerning mathematical properties, methods of calculations, and applications of topological indices in any area of interest. Moreover, papers on other topics in chemical graph theory are also welcome. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Topological indices
• Molecular descriptors
• Methods of calculations
• Algorithms
• QSP(A)R analysis
• Molecular graphs
• Complex molecules
• Nanostructures
• Resolving sets
• Different measures in networks
• Computational drugs
• Mathematical modelling in drug design
• Labelling to study chemical reaction networks