L(j, k)-labeling Number of Cactus Graph

[摘要] For j ≤ k, the L(j,k) -labelling problem arose from code assignment problem of computer wireless networks. That is, let j, k and m be positive numbers, an m-L(j, k) -labelling of a graph G is a mapping f: V(G) → [0, m] such that | f (u) - f (v) |≥ j if d (u, v) = 1, and | f (u) - f (v) |≥ k if d (u,v) = 2. The span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k) -labelling number of G, denoted by λjk (G), is the minimum span over all L( j, k)-labellings of G. In this paper, we introduce the L(j, k )- labelling numbers of Cactus graph for any positive real numbers j, k with j ≤ k.

[发布机构] Department of Computational Science, School of Science, Tianjin University of Technology and Education, Tianjin; 300222, China^1

[效力级别] 无线电电子学 [学科分类] 计算机科学（综合）

[关键词] Cactus graphs;Code assignments;Graph G;L(j ,k) labeling numbers;Positive numbers;Positive real