L(2,1)-Labeling: An Algorithmic Approachto Cycle Dominated Graphs

Let G be a connected, undirected graph. Distance two labeling or a 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)| is greater than or equal to 2 if x and y areadjacent and |f(x) − f(y)| is greater than or equal to 1 if x and y are at distance 2,for all x and y in V (G). The L(2,1)-labeling number (G) of G is the smallest numberk such that G has an L(2,1)-labeling f with max {f(v) : v 2 V (G) }is equal to k.In this paper, we present algorithms to get L(2,1)-labeling of cycle dominating graphslike Diamond graphs, nC4 with a common vertex and Books Bn and hence we findthe λ - number of these graphs.