Exceptional trivalent cayley graphs for dihedral groups

Abstract If n is divisible by at least three distinct primes, the dihedral group Dn can be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation of Dn for several families of n and for all admissible n < 120. All these graphs are trivalent, bipartite, Hamiltonian, of girth 6, and are regular representations of their groups. For each n, the isomorphism classes are determined and the graphs are described by a simple code.