While dealing with diversified concepts of applied mathematics, graphing is one of the powerful tools for representing and understanding objects and their relationships. For applying theoretical principles of graph theory into practical fields, graph invariants are determined and mapped to real-time problems. Graph invariants are properties like vertices, edges, diameter, and degree. Graph invariants act like a bridge between science and engineering as supporting tools or computational techniques especially in the areas of chemical, electrical, computer, and telecommunication engineering. Research in the area of graph theory is abundantly expanding in depth and breadth, and during the last 50 years, more than 2500 papers have been published in this domain, highlighting the importance of this subject area and its interest to researchers. This popularity is not only due to the mathematical challenges of graph theory but also due to the wide range of its applications.

Graph models are studied a lot in the form of theoretical material, but they become more challenging while dealing with real-life problems. Real-life scenarios can be graphically represented and in these representations graph invariants are significant to quantify the behaviour of problems. Graph distance is a well-known area with broad future scope due to fast communication over cloud and cluster computing. In addition, graph distances are used in the navigation of robots that locate themselves through distinct labelled nodes. An associated challenge in this respect is finding the fewest number of nodes to uniquely determine the position of a robot. Graph labelling is getting popular due to its broad spectrum of applications in coding theory, channel assignment, network addressing, circuit layouts and radio-astronomy, semantic web and protein, biological, honeycomb, butterfly and social networks. So far, labelling of static graphs is mostly identified whereas for dynamic graphs like temporal graphs, this area is still a challenge. Chemical graph theory is also one of the important areas under mathematical chemistry to uncover chemical phenomena and various physicochemical properties. Topological indices are often used as graph invariants to degrees of vertices, distances between vertices, symmetries. Comparative studies of such invariants may help their suitability in pharmacological activities.

The purpose of this Special Issue is to increase awareness and publication of recent developments in the area of graph properties, methods, and applications. Additionally, papers covering the applications of graph structures and models in computer science, chemistry, and engineering are welcome. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Graph labelling and colouring
• Graph algorithms and complexity theory
• Number theory and computer security
• Edge metric dimension
• Topological indices
• Mathematical chemistry
• Algebraic construction of extremal graph
• Graph convolutional networks