the line graph of a bipartite graph is perfect (see kőnig's theorem), but need not be bipartite as the example of the claw graph shows. the line graphs of bipartite graphs form one of the key building blocks of perfect graphs, used in the proof of the strong perfect graph theorem. a special case of these graphs are the rook's graphs, line graphs of complete bipartite graphs. like the line graphs of complete graphs, they can be characterized with one exception by their numbers of vertices, numbers of edges, and number of shared neighbors for adjacent and non-adjacent points. the one exceptional case is "l"("k"), which shares its parameters with the shrikhande graph. when both sides of the bipartition have the same number of vertices, these graphs are again strongly regular.