M. MURUGAN 1, P. SRIRAMAN 2 AND M. SURIYA 3 1.Tamil Nadu Open University, Department of Mathematics, School of Science, Chennai, INDIA
e-mail: muruganganesan@yahoo.in
2. Research Scholar, Department of Mathematics, School of Science, Tamil Nadu Open University,
Chennai, INDIA,
e-mail: psriraman2@gmail.com
3. SRM Institute of Science and Technology, Chennai, INDIA.
e-mail: suriyan2000@gmail.com
An 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 a distance 2, for all x and y in V (G). A k-L(2, 1)-labeling is an L(2, 1)-labeling f : V (G) → {0, 1, . . . , k}, and we are interested to find the minimum k among all possible labelings. This invariant, the minimum k, is known as the L(2, 1)-labeling number or λ-number and is denoted by λ(G). In this paper, we consider banana trees of type 1, banana trees of type 2 and path-union of k-copies of the star K1,n and find the λ-numbers of them.
