| L（1, 2）-edge-labelings for lattices |
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| 作者姓名： | HE Dan LIN Wen-song |
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| 作者单位： | Department of Mathematics, Southeast University, Nanjing 210096, China. |
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| 基金项目： | Supported -by the National Natural Science Foundation of China （10971025 and 10901035）. |
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| 摘 要： | 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 kThe λ j,k-number of G is the minimum m such that an m-L(j, k)-edge-labeling is admitted by GIn 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 λ j,k-numbers of these graphs are obtained.
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| 关 键 词： | 直尺 标号 正方形晶格 六方晶格 三角晶格 正整数 标记 相差 |
L(1, 2)-edge-labelings for lattices |
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| HE Dan LIN Wen-song.L(1, 2)-edge-labelings for lattices[J].Applied Mathematics A Journal of Chinese Universities,2014,29(2):230-240. |
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| Authors: | Dan He Wen-song Lin |
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| Institution: | 1. Department of Mathematics, Southeast University, Nanjing, 210096, China
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| Abstract: | 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 λ j,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 λ j,k ′-numbers of these graphs are obtained. |
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| Keywords: | L（j k）-edge-labeling line graph triangular lattice square lattice hexagonal lattice |
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