The notation K_m,n represents a specific type of bipartite graph in graph theory. In this graph, there are two distinct sets of vertices, one containing m vertices and the other containing n vertices. Each vertex in the first set is connected to every vertex in the second set, but there are no edges connecting vertices within the same set. Bipartite graphs like K_m,n are useful in various applications, including network flow problems and matching problems. They help model relationships between two different groups, such as students and courses, where connections represent enrollments.