Edge-combination classes of complete graphs

A systematic method of generating different combinations of edges, taken m at a time, in complete graphs, and classification of these edge combinations based on their topological structure, are discussed. In the process, a simple algorithm is presented for determining whether or not two given sets of edges are topologically equivalent. The listing of edge-combination classes has a significant bearing on some problems of realisation. The procedures given are all simple and routine and are suitable for computerisation.