Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks

Yu Guo; Qiong Wu

doi:doi:10.11648/j.ijssam.20210604.12

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Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks

Yu Guo, Qiong Wu

Published in International Journal of Systems Science and Applied Mathematics (Volume 6, Issue 4)

Received: 7 October 2021 Accepted: 1 November 2021 Published: 10 November 2021

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Abstract

Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ_(1,d)(G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 6, Issue 4)
DOI	10.11648/j.ijssam.20210604.12
Page(s)	120-124
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Circular L(1,d)-labeling, Book Graph, Code Assignment

References

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[2]	Yeh R K. (2005). A survey on labeling graphs with a condition at distance two [J]. Discrete Math. 306, 1217-1231.
[3]	Griggs J R, Jin X T. (2007). Recent Progress in Mathematics and Engineering on Optimal Graph Labellings with Distance Conditions [J]. Journal of Combinatorial Optimization. 14 (2-3), 249-257.
[4]	Jin X T, Yeh R K. (2005). Graph distance-dependent labeling related to code assignment in computer networks [J]. Naval Research Logistics. 52 (2): 159-164.
[5]	Niu, Q. (2007). L(j,k)-labeling of graph and edge span [D]. M. Phil. Thesis. Southeast University. Nanjing, China.
[6]	Griggs J R, Jin X T. (2005). Optimal channel assignments for lattices with conditions at distance two [J]. In Proc. 5th Int. Workshop on algorithms for wireless Mobile, Ad Hoc and Sensor Networks (W-MAN ’05), Denver, Colorado, April 4-8. IEEE Computer Society.
[7]	Shiu W C, Wu Q. (2013). L(j,k)-labeling number of direct product of path and cycle [J]. Acta Mathematica Sinica. 29 (8): 1437–1448.
[8]	Wu Q, Shiu W C. (2017). L(j,k)-labeling numbers of square of paths [J]. AKCE International Journal of Graphs and Combinatorics. 14 (3): 307–316.
[9]	Wu Q. (2018). L(j,k)-labeling number of generalized Petersen graph [J]. IOP Conference Series: Materials Science and Engineering. 466: 012084.
[10]	Wu Q. (2018). L(j,k)-labeling number of Cactus graph [J]. IOP Conference Series: Materials Science and Engineering. 466: 012082.
[11]	Liu L, Wu Q.(2020). L(1,2)-labeling numbers on square of cycles [J]. AKCE International Journal of Graphs and Combinatorics. 17 (3): 915-919.
[12]	Rao W L, Wu Q, Li Y. (2020). The L(1,2)-labeling numbers of Cartesian product of three paths [J]. Journal of Tianjin University of Technology and Education. 30 (3): 57-63.
[13]	Heuvel J, Leese R A, Shepherd M A. (1998). Graph labeling and radio channel assignment [J]. Journal of Graph Theory. 29 (4): 263-283.
[14]	Wu Q, Lin W S. (2010). Circular L(j,k)-labeling numbers of trees and products of graphs [J]. Southeast University. 26 (1): 142-145.
[15]	Wu Q, Shiu W C, Sun P K. (2014). Circular L(j,k)-labeling number of direct product of path and cycle [J]. Journal of Combinatorial Optimization. 27 (2): 355-368.
[16]	Wu Q, Shiu W C. (2017). Circular L(j,k)-labeling number of square of paths [J]. Journal of Combinatorics and Number Theory. 9 (1): 41-46.

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APA Style

Yu Guo, Qiong Wu. (2021). Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. International Journal of Systems Science and Applied Mathematics, 6(4), 120-124. https://doi.org/10.11648/j.ijssam.20210604.12

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ACS Style

Yu Guo; Qiong Wu. Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. Int. J. Syst. Sci. Appl. Math. 2021, 6(4), 120-124. doi: 10.11648/j.ijssam.20210604.12

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AMA Style

Yu Guo, Qiong Wu. Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. Int J Syst Sci Appl Math. 2021;6(4):120-124. doi: 10.11648/j.ijssam.20210604.12

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@article{10.11648/j.ijssam.20210604.12,
  author = {Yu Guo and Qiong Wu},
  title = {Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {6},
  number = {4},
  pages = {120-124},
  doi = {10.11648/j.ijssam.20210604.12},
  url = {https://doi.org/10.11648/j.ijssam.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20210604.12},
  abstract = {Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ(1,d) (G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.},
 year = {2021}
}

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TY  - JOUR
T1  - Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks
AU  - Yu Guo
AU  - Qiong Wu
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ijssam.20210604.12
DO  - 10.11648/j.ijssam.20210604.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 120
EP  - 124
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20210604.12
AB  - Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ(1,d) (G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.
VL  - 6
IS  - 4
ER  -

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Author Information

Yu Guo

Department of Computational Science, School of Science, Tianjin University of Technology and Education, Tianjin, China
Qiong Wu

Department of Computational Science, School of Science, Tianjin University of Technology and Education, Tianjin, China

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APA Style

Yu Guo, Qiong Wu. (2021). Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. International Journal of Systems Science and Applied Mathematics, 6(4), 120-124. https://doi.org/10.11648/j.ijssam.20210604.12

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ACS Style

Yu Guo; Qiong Wu. Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. Int. J. Syst. Sci. Appl. Math. 2021, 6(4), 120-124. doi: 10.11648/j.ijssam.20210604.12

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AMA Style

Yu Guo, Qiong Wu. Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks. Int J Syst Sci Appl Math. 2021;6(4):120-124. doi: 10.11648/j.ijssam.20210604.12

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@article{10.11648/j.ijssam.20210604.12,
  author = {Yu Guo and Qiong Wu},
  title = {Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {6},
  number = {4},
  pages = {120-124},
  doi = {10.11648/j.ijssam.20210604.12},
  url = {https://doi.org/10.11648/j.ijssam.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20210604.12},
  abstract = {Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ(1,d) (G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks
AU  - Yu Guo
AU  - Qiong Wu
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ijssam.20210604.12
DO  - 10.11648/j.ijssam.20210604.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 120
EP  - 124
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20210604.12
AB  - Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ(1,d) (G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.
VL  - 6
IS  - 4
ER  -

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