Advances and Applications in Discrete Mathematics

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BOOK THICKNESS OF TOTAL GRAPH, UNIT GRAPH AND DOUBLE TOTAL GRAPH OF COMMUTATIVE RINGS WITH GENUS AT MOST 2

Authors

  • Ngangom Rojitkumar Singh
  • Sanghita Dutta

Keywords:

fusible ring, unit graph, total graph, double total graph

DOI:

https://doi.org/10.17654/0974165824028

Abstract

In this paper, we determine the book thickness of planar and toroidal total graph, unit graph and double total graph of a finite commutative ring R with genus at most 2.

Received: March 3, 2024
Revised: May 28, 2024
Accepted: June 17, 2024

References

E. Ghashghaei and W. Wm. McGovern, Fusible rings, Comm. Algebra 45(3) (2017), 1151-1165.

F. Bernhart and P. C. Kainen, The book thickness of a graph, Journal of Combinatorial Theory 27(3) (1979), 320-331.

Hamid Reza Maimani, Cameron Wickham and Siamak Yassemi, Rings whose total graphs have genus at most one, Rocky Mountain J. Math. 42 (2012), 1551-1560.

M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, San Diego, 1980.

T. McKenzie and S. Overbay, Book thickness of toroidal zero divisor graphs, Afrika Matematica 28 (2017), 823-830. doi 10.1007/s13370-017-0487-7.

Ng. R. Singh and S. Dutta, The double total graph of a commutative ring, Advances and Applications in Discrete Mathematics 24 (2020), 99-115.

Ng. R. Singh and S. Dutta, A note on the double total graph and Communications in Mathematics and Applications 12 (2021), 203-211.

T. Tamizh Chelvam and T. Asir, On the genus of the total graph of a commutative ring, Comm. Algebra 41 (2013), 142-153.

R. Kala and S. Kavitha, Nilpotent graphs of genus one, Discrete Math. Algorithms Appl. 6(3) (2014), 1450037.

N. Ashrafi, H. R. Maimani, M. R. Pournaki and S. Yassemi, Unit graphs associated with rings, Comm. Algebra 38 (2010), 2851-2871.

H. Su, K. Noguchi and Y. Zhou, Finite commutative ring with higher genus unit graphs, J. Algebra Appl. 14 (2015), 1-14.

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, Upper Saddle River, 2001.

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Published

2024-06-28

Issue

Vol. 41 No. 5 (2024)

Section

Articles

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Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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How to Cite

BOOK THICKNESS OF TOTAL GRAPH, UNIT GRAPH AND DOUBLE TOTAL GRAPH OF COMMUTATIVE RINGS WITH GENUS AT MOST 2. (2024). Advances and Applications in Discrete Mathematics, 41(5), 411-427. https://doi.org/10.17654/0974165824028

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