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

L(3, 2, 1)-Labeling of Banana Trees AbstractAn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of West University of Timisoara - Mathematics de Gruyter

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

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References (3)

Publisher
de Gruyter
Copyright
© 2019 M. Murugan et al., published by Sciendo
ISSN
1841-3307
eISSN
1841-3307
DOI
10.2478/awutm-2019-0018
Publisher site
See Article on Publisher Site

Abstract

AbstractAn 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.

Journal

Annals of West University of Timisoara - Mathematics – de Gruyter

Published: Dec 1, 2019

Keywords: L (3, 2, 1)-labeling; Channel assignment; Banana Tree; k -number

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