<abstract xmlns="http://www.w3.org/1999/xhtml">

An <italic>L</italic>(3, 2, 1)-labeling of a graph <italic>G</italic> is an assignment <italic>f</italic> from the vertex set <italic>V</italic> (<italic>G</italic>) to the set of non-negative integers such that |<italic>f</italic> (<italic>x</italic>) − <italic>f</italic> (<italic>y</italic>) | ≥ 3 if <italic>x</italic> and <italic>y</italic> are adjacent, | <italic>f</italic> (<italic>x</italic>) − <italic>f</italic> (<italic>y</italic>) | ≥ 2 if <italic>x</italic> and <italic>y</italic> are at distance 2, and | <italic>f</italic> (<italic>x</italic>) − <italic>f</italic> (<italic>y</italic>) | ≥ 1 if <italic>x</italic> and <italic>y</italic> are at distance 3, for all <italic>x</italic> and <italic>y</italic> in <italic>V</italic> (<italic>G</italic>). The <italic>L</italic> (3, 2, 1)-labeling number <italic>k</italic> (<italic>G</italic>) of <italic>G</italic> is the smallest positive integer <italic>k</italic> such that <italic>G</italic> has an <italic>L</italic> (3, 2, 1)-labeling with <italic>k</italic> as the maximum label. In this paper, we consider banana trees of type 1, banana trees of type 2 and path-union of <italic>t</italic>-copies of the star <italic>K</italic>1<italic>,n</italic> and find the <italic>k</italic>-numbers of them.
</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.

<italic>L</italic>(3, 2, 1)-Labeling of Banana Trees

School of Science, Tamil Nadu Open University

Department of Mathematics, School of Science

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":{"italic":"L","content":"(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...

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

Published Online: Dec 21, 2020

Page range: 103 - 111

DOI: https://doi.org/10.2478/awutm-2019-0018

Keywords
(3, 2, 1)-labeling, Channel assignment, Banana Tree, -number

© 2019 M. Murugan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Dec 21, 2020

Page range: 103 - 111

DOI: https://doi.org/10.2478/awutm-2019-0018

Keywords(3, 2, 1)-labeling, Channel assignment, Banana Tree, -number

© 2019 M. Murugan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
(3, 2, 1)-labeling, Channel assignment, Banana Tree, -number