Initially, graph theory was used to solve recreational math problems. Nowadays, it has become a significant branch of interdisciplinary research between mathematics and other sciences. A graph is the most useful type of discrete structure due to its wide range of applications in almost all life research areas. A graph can be represented by a numeric number, a polynomial, a sequence of numbers, or a matrix that represents the entire graph. In the 18th century, Euler tried to solve the Seven Bridges of Königsberg and laid the foundation for graph theory by proving the first theorem. In 1956, Dijkstra’s algorithm was introduced to design efficient algorithms for finding optimal paths between vertices of graphs. Dijkstra's algorithm is now being used in road and computer networks. In the mid-’90s, the concept of graph labeling was introduced. In the last 60 years, over 200 types of graph labeling have been studied and almost 2500 articles have been published. Graph labeling is an assignment of integers to vertices or edges, or both, under certain conditions.

In parallel with graph labeling, topological graph theory was introduced as the four-color map problem. It was finally proven in 1976 by using computerized checking. In 1977, Bloom and Golomb studied the applications of graph labeling. They connected graph labeling to a wide range of applications such as x-ray crystallography, coding theory, radar, astronomy, circuit design, network, and communication design. Nowadays, research in graph labeling is increasingly expanding. According to depth research, a specific type of labeling is studied for more complex families of graphs or open problems. Meanwhile, in breadth research, more types of labeling are identified by the variation of graph invariants or by augmenting two existing types of labeling.

The aim of this Special Issue is to bring together original research and review articles discussing recent developments in graph labeling. Submissions should consider methods and applications in-depth and at stretch. Additionally, submissions should include the application of graph labeling in computer science, chemistry, and engineering.

Potential topics include but are not limited to the following:

• Graph labelings
• Degree diameter problems
• Distance in graphs
• Data structures and algorithm for labeling graphs
• Computational methods for labeling graphs
• Graph structure and applications
• Ramsey theory
• Locating numbers
• Graph labeling in topological indices
• Graph labeling in fuzzy graphs