L(j, k)-labeling Number of Generalized Petersen Graph

[摘要] For j ≤ k, the L(j,k) -labeling arose from code assignment problem in the computer wireless network. For positive real numbers j and k, an L(j, k) -labeling f of G is an assignment of numbers to vertices of G such that | f (u)- f (v)|≥ j if u, v are adjacent, and | f(u)-f(v)|≥ k if u, v are distance two apart. The span of f is the maximum difference among the numbers assigned by f. The L(j, k) -labeling number of G, denoted by λj k (G), is the minimum span over all L(j,k) -labeling of G . The generalized Petersen graph, denoted by G(n,k), is a graph with vertex set {u 0,u 1,...,un -1,v 0,v 1,...,vn -1} and edge set{(u.,u.+1), (ui ,vi .), (vi,vi +k): i = 0,•••,n-1}, where subscripts are to be taken modulo n and k ≤ [n/2]. In this paper, the author determines the L(j,k) -labeling numbers of generalized Petersen graphs G(n,1), G(n,2) and G(n, n/2), where n is even and 2j

[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] Code assignments;Edge-sets;Generalized Petersen graphs;L (j , k) labeling;L(j ,k) labeling numbers;Modulo-N;Positive real;Vertex set