The orientation number of two complete graphs with linkages Original Research Article

For a connected graph G containing no bridges, let image be the family of strong orientations of G; and for any image, we denote by image the diameter of D. The orientation number image of G is defined by image. In this paper, we study the orientation numbers of a family of graphs, denoted by image, that are obtained from the disjoint union of two complete graphs image and image by adding m edges linking them in an arbitrary manner. Define image. We prove that image and image. Let image. We evaluate the exact value of image when image and show that image for image.