On Ł ℘ , ℘ − 1 , … , 1 Labelings of Circulant Graphs

An - labeling of a simple graph is a mapping from the vertex set to such that , , where length of the shortest route connecting and is represented by . The smallest for which there exists a - labeling of is known as the labeling number of , and it is described by . We define - as the same as the - labeling if is one to one. The labeling number of represented by and is called minimum span. In this paper, we prove that the circulant graphs with specified generating sets admit - and - labeling and also find and . Moreover, we find the labeling number of any simple graph with diameter less than .