Distance two labelings of Cartesian products of complete graphs

作者：Lu, Damei; Lin, Wensong^*; Song, Zengmin

来源：Ars Combinatoria, 2012, 104: 33-40.

• L(2,1)-labeling
• lambda(2,1)-number
• Cartesian product

For two positive integers j and k with j >= k, an L(j, k)-labeling of a graph G is an assignment of nonnegative integers to V(G) such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L(j, k)-labeling of a graph G is the difference between the maximum and minimum integers used by it. The lambda(j,k)-number of G is the minimum span over all L(j, k)-labelings of G. This paper focuses on the lambda(2,1)-number of the Cartesian products of complete graphs. We completely determine the lambda(2,1)-numbers of the Cartesian products of three complete graphs K-n, K-m, and K-l for any three positive integers n, m, and l.

• 出版日期2012-4
• 单位东南大学; 南通大学