Circular L(j, k)-labeling Numbers of Trees and Products of Graphs
Qiong Wu, Wensong Lin · Journal of Southeast University · 2010
Let j, k and m be three positive integers, a circular m-L(j, k)-labeling of a graph G is a mapping f: V(G)→{0, 1, …, m-1}such that ∣f(u)-f(v)∣(subscript m)≥j if u and v are adjacent, and ∣f(u)-f(v)∣(subscript m)≥k if u and v are at distance two, where ∣a-b∣(subscript m)=min{∣a-b∣(subscript m)-∣a-b∣}. The minimum m such that there exists a circular m-L(j, k)-labeling of G is called the circular L(j, k)-labeling number of G and is denoted by σ(subscript j, k)(G). For any two positive integers j and k with j≤k, the circular L(j, k)-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.