2189	 Generation of Rosary Permutations Expressed in Hamiltonian Circuits	 Systematic generation of a specific class of permutations fundamental to scheduling problems is described. In a nonoriented complete graph with n vertices Hamitonian circuits equivalent to . n - specific permutations of n elements termed rosary permutations can be defined. Each of them corresponds to two circular permutations which mirror-image each other and is generated successively by a number system covering ... n- sets of edges. Every set of edges E k E k k k n- is determined recursively by constructing a Hamiltonian circuit with k vertices from a Hamiltonian circuit with k- vertices starting with the Hamiltonian circuit of vertices. The basic operation consists of transposition of a pair of adjacent vertices where the position of the pair in the permutation is determined by E k . Two algorithms treating the same example for five vertices are presented. It is very easy to derive all possible n permutations from the . n - rosary permutations be cycling the permutations and by taking them in the reverse order-procedures which can be performed fairly efficiently by computer. permutation graph theory scheduling combinatorial algebra
