ON THE SYMMETRIES OF SOME CLASSES OF RECURSIVE CIRCULANT GRAPHS

A recursive-circulant G(n; d) is defined to be a circulant graph with n vertices and jumps of powers of d. G(n; d) is vertex-transitive, and has some strong hamiltonian properties. G(n; d) has a recursive structure when n = cdm, 1 ? c < d [Theoret. Comput. Sci. 244 (2000) 35-62]. In this paper, we will find the automorphism group of some classes of recursive-circulant graphs. In particular, we will find that the automorphism group of G(2m; 4) is isomorphic with the group D2·2m, the dihedral group of order 2m+1.