-labeling numbers of square of paths

Abstract

For , the -labeling arose from code assignment problem. That is, let , and be positive numbers, an --labeling of a graph is a mapping such that if , and if . The span of is the difference between the maximum and the minimum numbers assigned by . The -labeling number of , denoted by , is the minimum span over all -labelings of . The th power of an undirected graph is the graph with the vertex set of in which two vertices are adjacent when their distance in is at most . In this paper, the -labeling numbers of are determined for .

Keywords

• -labeling
• path
• square of path
• code assignment