Improved upper bound on the L(2, 1)-labeling of Cartesian sum of graphs
نویسندگان
چکیده
AnL(2, 1)-labeling of a graphG is defined as a function f from the vertex setV (G) into the nonnegative integers such that for any two vertices x, y, |f (x)−f (y)| ≥ 2 if d(x, y) = 1 and |f (x)− f (y)| ≥ 1 if d(x, y) = 2, where d(x, y) is the distance between x and y in G. The L(2, 1)-labeling number λ2,1(G) of G is the smallest number k such that G has an L(2, 1)-labeling with k = max{f (x)|x ∈ V (G)}. In this paper, we consider the graph formed by the Cartesian sum of two graphs and give new upper bound of the L(2, 1)-labeling number, which improves the bound obtained by [Z.D.Shao, D.Zhang, The L(2, 1)-labeling on Cartesian sum of graphs, Applied Mathematics Letters 21(2008) 843-848.] significantly. AMS subject classification: 05C15, 05C78.
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