A distance-regular graph is a type of graph characterized by a uniform structure in terms of distances between vertices. In these graphs, the number of vertices at a given distance from any vertex is consistent throughout the graph. This property allows for a systematic way to analyze the relationships and connections within the graph. Distance-regular graphs are defined by specific parameters, including the number of vertices, the degree of each vertex, and the number of vertices at each distance. They are often studied in combinatorics and have applications in areas such as network theory and coding theory.