L(2, 1) -Labeling for Subdivisions of Some 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 is an element of V(G)} = k. In this paper, we construct L(2, 1)-labeling of subdivisions of cycle dominated graphs like subdivided Double Fans, subdivided nC(alpha) with a common vertex and subdivided Books B-n, and hence we find the lambda-number of these graphs.