On $ {L}(2,1) $-labelings of some products of oriented cycles

Lucas Colucci; Ervin Győri

doi:10.3934/mfc.2021029

Article Contents

2022, Volume 5, Issue 1: 67-74. Doi: 10.3934/mfc.2021029

This issue Previous Article Bound state solutions for fractional Schrödinger-Poisson systems Next Article

On $ {L}(2,1) $-labelings of some products of oriented cycles

Lucas Colucci^1, , and
Ervin Győri^2,

1.
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13–15, 1053 Budapest, Hungary
2.
Central European University, Department of Mathematics and its Applications, Nádor u. 9, 1051 Budapest, Hungary

^* Corresponding author: Lucas Colucci
^* Corresponding author: Lucas Colucci

Received: December 2019

Revised: July 2021

Early access: November 2021

Published: February 2022

The first author is partially supported by the National Research, Development and Innovation, NKFIH grant K 116769. The second author is partially supported by the National Research, Development and Innovation, NKFIH grants K 116769 and SNN 117879

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Abstract

We refine two results of Jiang, Shao and Vesel on the $ L(2,1) $-labeling number $ \lambda $ of the Cartesian and the strong product of two oriented cycles. For the Cartesian product, we compute the exact value of $ \lambda(\overrightarrow{C_m} \square \overrightarrow{C_n}) $ for $ m $, $ n \geq 40 $; in the case of strong product, we either compute the exact value or establish a gap of size one for $ \lambda(\overrightarrow{C_m} \boxtimes \overrightarrow{C_n}) $ for $ m $, $ n \geq 48 $.

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Mathematics Subject Classification: Primary: 05C15, 05C78; Secondary: 05C20.

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Figure 1. The Cartesian product of $\overrightarrow {{P_3}} $ and $\overrightarrow {{P_4}} $

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Figure 2. The strong product of $\overrightarrow {{P_3}} $ and $\overrightarrow {{P_4}} $

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Figure 3. A $ \overrightarrow{P_4} \boxtimes \overrightarrow{P_4} $ subgraph of $ \overrightarrow{C_m} \boxtimes \overrightarrow{C_n} $

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References

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