For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edg...For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.展开更多
For positive 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 uv∈E（G）, and ｜f（u）-f（v）｜≥k if d（u,v）=2. Then the span of f is the di...For positive 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 uv∈E（G）, and ｜f（u）-f（v）｜≥k if d（u,v）=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L（j,k）-number of G, denoted by λj,k（G）, is the minimum span over all L（j,k）-labelings of G. In this paper, we give some results about the L（j,k）-number of the direct product of a path and a cycle for j≤k.展开更多
基金Supported by the National Natural Science Foundation of China(10971025 and 10901035)
文摘For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.
基金Supported by National Natural Science Foundation of China (No.10301010 and No.60673048)Natural Science Foundation of Education Ministry of Anhui Province (NO.KJ2007B124).
基金Supported by Faculty Research Grant, Hong Kong Baptist University
文摘For positive 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 uv∈E（G）, and ｜f（u）-f（v）｜≥k if d（u,v）=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L（j,k）-number of G, denoted by λj,k（G）, is the minimum span over all L（j,k）-labelings of G. In this paper, we give some results about the L（j,k）-number of the direct product of a path and a cycle for j≤k.
基金The project was supported by the Cooperation Foun-dation of Yunnan Province-Academy and Province-University (2003AFBBA00A032)National Nature Sciences Foundation(30560174).
