L(3, 2, 1)-Labeling of Banana Trees

Abstract

An L(3, 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) | ≥ 3 if x and y are adjacent, | f (x) − f (y) | ≥ 2 if x and y are at distance 2, and | f (x) − f (y) | ≥ 1 if x and y are at distance 3, for all x and y in V (G). The L (3, 2, 1)-labeling number k (G) of G is the smallest positive integer k such that G has an L (3, 2, 1)-labeling with k as the maximum label. In this paper, we consider banana trees of type 1, banana trees of type 2 and path-union of t-copies of the star K1,n and find the k-numbers of them.

Keywords

• l(3, 2, 1)-labeling
• channel assignment
• banana tree
• k-number