Product graphs for given subgroups of the wreath product of two groups, I

AbstractFrucht [1] gave a method for constructing for each arbitrarily given group a graph whose automorphism group is isomorphic to the prescribed group. Constructions of “product” graphs whose automorphism groups are given subgroups of the wreath product of two groups are given. For S2 wr G, comprehensive results are given for all subgroups of S2 wr G containing 1 × G. A concept of graph product which is a generalization of Imrich's definition [2] is employed