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

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 K 1 ,n and find the k -numbers of them.

Abstract licence: CC BY-NC-ND

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