【摘 要】
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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 adjace
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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 receive labels differ by at least j, and edges which are distance two apart receive labels differ by at least k.The λj,k-number of G is the minimum m such that an m-L(j, k)-edgelabeling is admitted by G.In this article, we study the L(1, 2)-edge-labeling for paths,cycles, complete graphs, complete multipartite graphs, infinite r-regular trees ,wheels, the hexagonal lattice, the square lattice and the triangular lattice.
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