A distance-regular graph is a type of graph characterized by its uniform structure in terms of distances between vertices. In such graphs, for any two vertices at a certain distance, the number of vertices at each distance from them is constant. This property allows for a predictable and regular pattern in the connections between vertices. These graphs are often studied in the field of graph theory and have applications in various areas, including combinatorics and network design. Examples of distance-regular graphs include strongly regular graphs and Hamming graphs, which exhibit specific regularity and symmetry properties.