The L ( 2 , 1 ) - Labeling Problem on Graphs by
نویسنده
چکیده
An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that jf(x) f(y)j 2 if d(x; y) = 1 and jf(x) f(y)j 1 if d(x; y) = 2. The L(2; 1)-labeling number (G) of G is the smallest number k such that G has a L(2; 1)-labeling with maxff(v) : v 2 V (G)g = k. In this paper, we give exact formulas of (G[H) and (G+H). We also prove that (G) 2 + for any graph G of maximum degree . For OSF-chordal graphs, the upper bound can be reduced to (G) 2 + 1. For SF-chordal graphs, the upper bound can be reduced to (G) + 2 (G) 2. Finally, we present a polynomial time algorithm to determine (T ) for a tree T .
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