Weak sense of direction labelings and graph embeddings Original Research Article

An edge-labeling image for a directed graph image has a weak sense of direction (WSD) if there is a function image that satisfies the condition that for any node image and for any two label sequences image and image generated by non-trivial walks on image starting at image, image if and only if the two walks end at the same node. The function image is referred to as a coding function of image. The weak sense of direction number of image, WSDimage, is the smallest integer image so that image has a WSD-labeling that uses image labels. It is known that WSDimageimage, where image is the maximum outdegree of image.