Identity orientation of complete bipartite graphs Original Research Article

An identity orientation of a graph image is an orientation of some of the edges of E such that the resulting partially oriented graph has no automorphism other than the identity. We show that the complete bipartite graph image, with image, does not have an identity orientation if image. We also show that if image then image does have an identity orientation. These results improve the previous bounds obtained by Harary and Jacobson (Discuss. Math. - Graph Theory 21 (2001) 158). We use these results to determine exactly the values of t for which an identity orientation of image exists for image.