L(3, 2, 1)-Labeling of Banana Trees
2019 ◽
Vol 57
(2)
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pp. 103-111
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 K 1 ,n and find the k-numbers of them.
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2001 ◽
Vol 8
(1)
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pp. 70-82
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1994 ◽
Vol 71
(06)
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pp. 731-736
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