The L( 2,1)-labelings of the similarity ladders
DU Jua · Journal of Liaoning University · 2013
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 | f(u)- f(v) | ≥2 if d(u,v) = 1,and | f(u)- f(v) | ≥1 if d(u,v) = 2.Without loss of generality,we let the least label be 0.The L(2,1)-labeling numberλ(G) of G is the smallest number over the spans max{ f(v); v∈V(G) } of all L(2,1)-labelings of G.In this paper,we define the similarity ladders,and completely determine its L(2,1)-labeling number.