科研之友
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摘要
An L(2, 1)-labelling of a graph G is a function from the vertex set V(G) to the set of all nonnegative integers such that vertical bar f(u) - f (v)vertical bar >= 2 if d(G)(u, v) = 1 and vertical bar f(u) - f (v)vertical bar >= 1 if d(G)(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by lambda(C), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598-603].
