A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G.The path covering number of G, denoted by P(G), is the minimum number of paths in a path covering of G.An k-L(2, 1)-labelingofa graph G is a mapping f from V(G) to the set {0,1,…,k} such that |f(u)-f(v)| ≥ 2 if dG(u,v) =1 and |f(u)-f(v)| ≥ 1 if dG(u, v) =2.The L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has a k-L(2, 1)-labeling.