Circular L(j, k)-Labeling Numbers of Square of Paths

摘要

Let j, k and σ be positive numbers, a circular σ-L(j， k)-labeling of a graph G is a function f : V(G) →[0,σ） such that | f(u) - f(v)|σ > j if u and v are adjacent， and |f(u) — f(v)|σ > k if u and v are at distance two， where |a - b|σ = min{|α - b|, σ - |α - b|}. The minimum σ such that there exist a circular σ-L(j， k）-labeling of G is called the circular-L(j, k)-labeling number of G and is denoted by σ_(j,k)(G). The k-th power G~k of an undirected graph G is a graph with the same set of vertices and an edge between two vertices when their distance in G is at most k. In this paper, the circular L(j, k)-labeling numbers of P_n~2 are determined.