Orthogonal covers by multiplication graphs Original Research Article

Let image be the complete oriented graph on the finite set of vertices image. A family image of spanning subgraphs of image is an orthogonal cover provided every arrow of image occurs in exactly one image and for every two elements image, the graphs image and image have exactly one arrow in common. Gronau, Grüttmüller, Hartmann, Leck and Leck [H.-D.O.F. Gronau, M. Grüttmüller, S. Hartmann, U. Leck, V. Leck, On orthogonal double covers of graphs, Designs, Codes and Cryptography 27 (2002) 49–91] have observed that if image has the structure of a finite ring and if image is such that both image and image are units, then the family, obtained by taking for image the multiplication graph of image and for image the rotation of image by image, defines an orthogonal cover on image. In this article we assume that image is a finite abelian group and proceed to