Chemical graph theory can be thought of as a mathematical representation of molecules and chemical structures. In today's world, molecular topology, in conjunction with graph theory and physical-chemical measures such as covalent and ionic potentials, boiling and melting point, and electronic density, provides a comprehensive picture of molecular structures. The mathematical simplicity in attributing numbers to chemical structures by counting vertices, neighbors, distance, eigenvalues, eccentricity, reciprocal relationships, and so on sparked interest and motivation to study graph theory. The ability of the resulting information to model and predict chemical properties has been widely demonstrated, ranging from simple structures to novel nano-chemical structures of extended carbon systems (junctions, nanotubes, fullerenes, graphenes, etc.). Furthermore, molecular topology by chemical graph theory appears to explain biological activity by modeling toxicants. Topological indices, energy, and domination are important graph invariants in the modeling and characteristics of chemical networks and structures.

Due to the vast applications and growth potential of graph invariants and chemical graph theory, a novel face index was recently introduced in the newest version of Mathematics in 2020, and it gained interest and attracted researchers to study this new variant in 2021. This parameter presented the idea of using the methodology of face degree instead of traditional vertex or edge degree and related this to acquire energy of a chemical structure. This idea will help to gain more applications of graph theory in different fields of engineering or applied sciences.

This Special Issue aims to encourage leading researchers and scientists working in this interdisciplinary field to relate new methods, techniques, and computing algorithms to various theoretical and computational aspects of graph invariants applied to chemical structures, as well as to fill the gap between theoretical and applied sciences by identifying contemporary applications. We welcome original research and review articles.

Potential topics include but are not limited to the following:

• Graph algorithms and complexity theory
• Spectral graph theory and applications
• Metric-based parameters
• Distance-based notions of graphs
• Number theory and computer security
• Algebraic construction of the extremal graph
• Face index
• Molecular topological indices
• Entropy of graphs
• Polynomial-based topics of graphs