- Previous Article
- MFC Home
- This Issue
-
Next Article
Bound state solutions for fractional Schrödinger-Poisson systems
February
2022, 5(1): 67-74.
doi: 10.3934/mfc.2021029
On $ {L}(2,1) $-labelings of some products of oriented cycles
| 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 |
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 $.
Keywords:
$ L(2,1) $-labeling,
oriented graphs,
graph products,
Cartesian product of graphs,
strong product of graphs.
Mathematics Subject Classification:
Primary: 05C15, 05C78; Secondary: 05C20.
Citation:
Lucas Colucci, Ervin Győri. On $ {L}(2,1) $-labelings of some products of oriented cycles. Mathematical Foundations of Computing,
2022, 5
(1)
: 67-74.
doi: 10.3934/mfc.2021029
![]()
References:
| [1] |
T. Calamoneri, The ${L}(h, k) $-labelling problem: An updated survey and annotated bibliography, 2014, Available on http://www.dsi.uniroma1.it/calamo/PDF-FILES/survey.pdf. |
| [2] |
G. J. Chang and S.-C. Liaw,
The ${L}(2, 1) $-labeling problem on ditrees, Ars Combin., 66 (2003), 23-31.
|
| [3] |
W. K. Hale,
Frequency assignment: Theory and applications, Proceedings of the IEEE, 68 (1980), 1497-1514.
doi: 10.1109/PROC.1980.11899. |
| [4] |
Z. Shao, H. Jiang and A. Vesel,
${L}(2, 1) $-labeling of the cartesian and strong product of two directed cycles, Mathematical Foundations of Computing, 1 (2018), 49-61.
doi: 10.3934/mfc.2018003. |
| [5] |
J. J. Sylvester, et al, Mathematical questions with their solutions, Educational times 41, 21 (1884), 6pp. |
| [6] |
K. -C. Yeh, Labeling Graphs with a Condition at Distance Two, PhD thesis, University of South Carolina, 1990. |
| [7] |
R. K. Yeh,
A survey on labeling graphs with a condition at distance two, Discrete Math., 306 (2006), 1217-1231.
doi: 10.1016/j.disc.2005.11.029. |
show all references
References:
| [1] |
T. Calamoneri, The ${L}(h, k) $-labelling problem: An updated survey and annotated bibliography, 2014, Available on http://www.dsi.uniroma1.it/calamo/PDF-FILES/survey.pdf. |
| [2] |
G. J. Chang and S.-C. Liaw,
The ${L}(2, 1) $-labeling problem on ditrees, Ars Combin., 66 (2003), 23-31.
|
| [3] |
W. K. Hale,
Frequency assignment: Theory and applications, Proceedings of the IEEE, 68 (1980), 1497-1514.
doi: 10.1109/PROC.1980.11899. |
| [4] |
Z. Shao, H. Jiang and A. Vesel,
${L}(2, 1) $-labeling of the cartesian and strong product of two directed cycles, Mathematical Foundations of Computing, 1 (2018), 49-61.
doi: 10.3934/mfc.2018003. |
| [5] |
J. J. Sylvester, et al, Mathematical questions with their solutions, Educational times 41, 21 (1884), 6pp. |
| [6] |
K. -C. Yeh, Labeling Graphs with a Condition at Distance Two, PhD thesis, University of South Carolina, 1990. |
| [7] |
R. K. Yeh,
A survey on labeling graphs with a condition at distance two, Discrete Math., 306 (2006), 1217-1231.
doi: 10.1016/j.disc.2005.11.029. |
Figure 3.
A $ \overrightarrow{P_4} \boxtimes \overrightarrow{P_4} $ subgraph of $ \overrightarrow{C_m} \boxtimes \overrightarrow{C_n} $
| [1] |
Zehui Shao, Huiqin Jiang, Aleksander Vesel. L(2, 1)-labeling of the Cartesian and strong product of two directed cycles. Mathematical Foundations of Computing, 2018, 1 (1) : 49-61. doi: 10.3934/mfc.2018003 |
| [2] |
Shuangliang Tian, Ping Chen, Yabin Shao, Qian Wang. Adjacent vertex distinguishing edge-colorings and total-colorings of the Cartesian product of graphs. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 49-58. doi: 10.3934/naco.2014.4.49 |
| [3] |
Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$-norm on graphs. Inverse Problems and Imaging, 2013, 7 (3) : 907-926. doi: 10.3934/ipi.2013.7.907 |
| [4] |
Christine A. Kelley, Deepak Sridhara, Joachim Rosenthal. Zig-zag and replacement product graphs and LDPC codes. Advances in Mathematics of Communications, 2008, 2 (4) : 347-372. doi: 10.3934/amc.2008.2.347 |
| [5] |
Serge Nicaise. Control and stabilization of 2 × 2 hyperbolic systems on graphs. Mathematical Control and Related Fields, 2017, 7 (1) : 53-72. doi: 10.3934/mcrf.2017004 |
| [6] |
Barton E. Lee. Consensus and voting on large graphs: An application of graph limit theory. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1719-1744. doi: 10.3934/dcds.2018071 |
| [7] |
Jennifer D. Key, Washiela Fish, Eric Mwambene. Codes from the incidence matrices and line graphs of Hamming graphs $H^k(n,2)$ for $k \geq 2$. Advances in Mathematics of Communications, 2011, 5 (2) : 373-394. doi: 10.3934/amc.2011.5.373 |
| [8] |
Litao Guo, Bernard L. S. Lin. Vulnerability of super connected split graphs and bisplit graphs. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1179-1185. doi: 10.3934/dcdss.2019081 |
| [9] |
Hirobumi Mizuno, Iwao Sato. L-functions and the Selberg trace formulas for semiregular bipartite graphs. Conference Publications, 2003, 2003 (Special) : 638-646. doi: 10.3934/proc.2003.2003.638 |
| [10] |
Srimathy Srinivasan, Andrew Thangaraj. Codes on planar Tanner graphs. Advances in Mathematics of Communications, 2012, 6 (2) : 131-163. doi: 10.3934/amc.2012.6.131 |
| [11] |
Cristina M. Ballantine. Ramanujan type graphs and bigraphs. Conference Publications, 2003, 2003 (Special) : 78-82. doi: 10.3934/proc.2003.2003.78 |
| [12] |
Daniele D'angeli, Alfredo Donno, Michel Matter, Tatiana Nagnibeda. Schreier graphs of the Basilica group. Journal of Modern Dynamics, 2010, 4 (1) : 167-205. doi: 10.3934/jmd.2010.4.167 |
| [13] |
James B. Kennedy, Jonathan Rohleder. On the hot spots of quantum graphs. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3029-3063. doi: 10.3934/cpaa.2021095 |
| [14] |
Yong Lin, Gábor Lippner, Dan Mangoubi, Shing-Tung Yau. Nodal geometry of graphs on surfaces. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1291-1298. doi: 10.3934/dcds.2010.28.1291 |
| [15] |
Rodrigo P. Pacheco, Rafael O. Ruggiero. On C1, β density of metrics without invariant graphs. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 247-261. doi: 10.3934/dcds.2018012 |
| [16] |
Dina Ghinelli, Jennifer D. Key. Codes from incidence matrices and line graphs of Paley graphs. Advances in Mathematics of Communications, 2011, 5 (1) : 93-108. doi: 10.3934/amc.2011.5.93 |
| [17] |
Wooyeon Kim, Seonhee Lim. Notes on the values of volume entropy of graphs. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5117-5129. doi: 10.3934/dcds.2020221 |
| [18] |
Renato Iturriaga, Héctor Sánchez Morgado. The Lax-Oleinik semigroup on graphs. Networks and Heterogeneous Media, 2017, 12 (4) : 643-662. doi: 10.3934/nhm.2017026 |
| [19] |
Thomas Zaslavsky. Quasigroup associativity and biased expansion graphs. Electronic Research Announcements, 2006, 12: 13-18. |
| [20] |
Deng Lu, Maria De Iorio, Ajay Jasra, Gary L. Rosner. Bayesian inference for latent chain graphs. Foundations of Data Science, 2020, 2 (1) : 35-54. doi: 10.3934/fods.2020003 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]