L(2,1)-Labeling for Subdivisions of Cycle Dominated Graphs

Let G(V,E) be a simple, finite, connected, undirected graph. Distance two labeling or L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of non-negative integers such that |f(x)-f(y)| >= 2 if x and y are adjacent and |f(x)-f(y)| >= 1 if x and y are at distance 2, for all x and y in V(G). The L(2,1)-labeling number lambda(G) of G is the smallest number k such that G has an L(2,1)-labeling f with max{f(v):v in V(G)}=k. In this paper, we construct L(2,1)-labeling of subdivisions of cycle dominated graphs like subdivided Double Fans, subdivided nCalpha with a common vertex and subdivided Books Bn and hence we find the λ-number of these graphs.