Resolvable 4-cycle group divisible designs with two associate classes: Part size even Original Research Article

Let image denote the graph on a vertices with image edges between every pair of vertices. Take p copies of this graph image, and join each pair of vertices in different copies with image edges. The resulting graph is denoted by image, a graph that was of particular interest to Bose and Shimamoto in their study of group divisible designs with two associate classes. The existence of z-cycle decompositions of this graph have been found when image. In this paper we consider resolvable decompositions, finding necessary and sufficient conditions for a 4-cycle factorization of image (when image is even) or of image minus a 1-factor (when image is odd) whenever a is even.