A complete bipartite graph, denoted as K(m,n), is a type of graph that consists of two distinct sets of vertices. Each vertex in the first set, containing m vertices, is connected to every vertex in the second set, which contains n vertices. However, there are no edges connecting vertices within the same set. In a complete bipartite graph, the total number of edges is equal to the product of the sizes of the two sets, resulting in m * n edges. This structure is useful in various fields, including computer science and network theory, for modeling relationships between two different groups.