Many real-world situations can conveniently be described by means of a diagram consisting of a set of points together with lines joining certain pairs of these points. For example, the vertices could represent people with edges joining pairs of friends; or the vertices might be communication centers with edges representing communication links. In such diagrams, one is mainly interested in whether two given vertices are joined by an edge; the manner in which they are joined is immaterial. A mathematical abstraction of situations of this type gives rise to the concept of a graph. There are many interesting aspects for study of graph theory.

Graph theory problems exist in engineering, information technology, chemistry, and physics. The concept of power domination came into existence from optimization problems faced by the electrical power system industry. The problem of uniquely determining the location of an intruder in a network, robot navigation, and problems in pharmaceutical chemistry have led to several invariants in extremal and topological graph theory and metric dimension of graphs. The spectra of graphs, or of certain matrices which are closely related to adjacency matrices, appear in several problems in statistical physics. Graph spectra appear in internet technologies, pattern recognition, and computer vision and in many other areas. Another field which has much to do with graph theory is combinatorial optimization. Networks appearing in biology have been analyzed by spectra of normalized graph Laplacian.

This Special Issue aims to offer an opportunity to researchers to share their original work and ideas in investigating various graph theory problems and their applications in engineering, information technology, chemistry, and other sciences. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Extremal problems in graph theory
• Topological indices
• Energy of molecular graphs
• Simple, Laplacian, and Laplacian-like energies of molecular graphs
• Spectral graph theory in chemistry
• Graph labeling
• Metric dimension and related invariants
• Domination in graphs