Many block designs correspond to decompositions of complete graphs.
In particular, a Steiner triple system is equivalent to a K 3 decomposition of K n , and a directed triple system is equivalent to a 3-circuit decomposition of the complete directed graph. In broadest terms, my area of specialty in combinatorics is the study of automorphisms of graph decompositions. Cyclic and rotational automorphisms have been used to establish the existence of several types of graph and directed graph decompositions. See my list of publications for more details. A permutation is bicyclic if it consists of two disjoint cycles.