Combinatorial graphs are mathematical structures used to study relationships between objects. They consist of vertices (or nodes) connected by edges, representing connections or interactions. These graphs can model various real-world scenarios, such as social networks, transportation systems, and computer networks. In combinatorial graph theory, researchers explore properties like connectivity, paths, and cycles. They also analyze different types of graphs, such as bipartite graphs and planar graphs, to understand their unique characteristics. This field has applications in computer science, optimization, and operations research, making it a vital area of study in mathematics.