Optimal radio labellings of complete image-ary trees Original Research Article

A radio labelling of a connected graph image is a mapping image such that image for each pair of distinct vertices image, where image is the diameter of image and image the distance between image and image. The span of image is defined as image, and the radio number of image is the minimum span of a radio labelling of image. A complete image-ary tree (image) is a rooted tree such that each vertex of degree greater than one has exactly image children and all degree-one vertices are of equal distance (height) to the root. In this paper we determine the radio number of the complete image-ary tree for any image with any height and construct explicitly an optimal radio labelling.