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Year 2024, Volume: 36 Issue: 36, 157 - 183, 12.07.2024
https://doi.org/10.24330/ieja.1478624

Abstract

References

  • D. D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, 159 (1993), 500-514.
  • D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434-447.
  • I. Beck, Coloring of commutative rings, J. Algebra, 116 (1988), 208-226.
  • C. P. Mooney, On gracefully and harmoniously labeling zero-divisor graphs, in Rings, Monoids and Module Theory, Springer Proc. Math. Stat., Springer, Singapore, 382 (2021), 239-260.
  • S. P. Redmond, On zero-divisor graphs of small finite commutative rings, Discrete Math., 307(9-10) (2007), 1155-1166.
  • S. P. Redmond, Corrigendum to: “On zero-divisor graphs of small finite commutative rings” [Discrete Math. 307(9-10) (2007), 1155–1166], Discrete Math., 307(21) (2007), 2449-2452.
  • J. Sedlacek, On magic graphs, Math. Slovaca, 26(4) (1976), 329-335.
  • B. M. Stewart, Magic graphs, Canadian J. Math., 18 (1966), 1031-1059.
  • B. M. Stewart, Supermagic complete graphs, Canadian J. Math., 19 (1967), 427-438.

On magic type labelings of zero-divisor graphs

Year 2024, Volume: 36 Issue: 36, 157 - 183, 12.07.2024
https://doi.org/10.24330/ieja.1478624

Abstract

In this article, we investigate magic type labelings of zero-divisor graphs. In particular, we turn our attention to semi-magic, magic, and super-magic labelings. We are able to construct infinitely many rings which admit these magic type labelings as well as infinitely many rings which do not have these magic type labeling. We further proceed to classify the magic type labeling properties for all of the rings which have zero-divisor graphs with up to 14 vertices. We then conclude with some conjectures about how these patterns may extend for larger zero-divisor graphs.

References

  • D. D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, 159 (1993), 500-514.
  • D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434-447.
  • I. Beck, Coloring of commutative rings, J. Algebra, 116 (1988), 208-226.
  • C. P. Mooney, On gracefully and harmoniously labeling zero-divisor graphs, in Rings, Monoids and Module Theory, Springer Proc. Math. Stat., Springer, Singapore, 382 (2021), 239-260.
  • S. P. Redmond, On zero-divisor graphs of small finite commutative rings, Discrete Math., 307(9-10) (2007), 1155-1166.
  • S. P. Redmond, Corrigendum to: “On zero-divisor graphs of small finite commutative rings” [Discrete Math. 307(9-10) (2007), 1155–1166], Discrete Math., 307(21) (2007), 2449-2452.
  • J. Sedlacek, On magic graphs, Math. Slovaca, 26(4) (1976), 329-335.
  • B. M. Stewart, Magic graphs, Canadian J. Math., 18 (1966), 1031-1059.
  • B. M. Stewart, Supermagic complete graphs, Canadian J. Math., 19 (1967), 427-438.
There are 9 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Jackson Feggestad This is me

Jacob Halvorson This is me

Christopher Park Mooney

Noah Royce This is me

Nathaen Wanta This is me

Early Pub Date May 5, 2024
Publication Date July 12, 2024
Published in Issue Year 2024 Volume: 36 Issue: 36

Cite

APA Feggestad, J., Halvorson, J., Mooney, C. P., Royce, N., et al. (2024). On magic type labelings of zero-divisor graphs. International Electronic Journal of Algebra, 36(36), 157-183. https://doi.org/10.24330/ieja.1478624
AMA Feggestad J, Halvorson J, Mooney CP, Royce N, Wanta N. On magic type labelings of zero-divisor graphs. IEJA. July 2024;36(36):157-183. doi:10.24330/ieja.1478624
Chicago Feggestad, Jackson, Jacob Halvorson, Christopher Park Mooney, Noah Royce, and Nathaen Wanta. “On Magic Type Labelings of Zero-Divisor Graphs”. International Electronic Journal of Algebra 36, no. 36 (July 2024): 157-83. https://doi.org/10.24330/ieja.1478624.
EndNote Feggestad J, Halvorson J, Mooney CP, Royce N, Wanta N (July 1, 2024) On magic type labelings of zero-divisor graphs. International Electronic Journal of Algebra 36 36 157–183.
IEEE J. Feggestad, J. Halvorson, C. P. Mooney, N. Royce, and N. Wanta, “On magic type labelings of zero-divisor graphs”, IEJA, vol. 36, no. 36, pp. 157–183, 2024, doi: 10.24330/ieja.1478624.
ISNAD Feggestad, Jackson et al. “On Magic Type Labelings of Zero-Divisor Graphs”. International Electronic Journal of Algebra 36/36 (July 2024), 157-183. https://doi.org/10.24330/ieja.1478624.
JAMA Feggestad J, Halvorson J, Mooney CP, Royce N, Wanta N. On magic type labelings of zero-divisor graphs. IEJA. 2024;36:157–183.
MLA Feggestad, Jackson et al. “On Magic Type Labelings of Zero-Divisor Graphs”. International Electronic Journal of Algebra, vol. 36, no. 36, 2024, pp. 157-83, doi:10.24330/ieja.1478624.
Vancouver Feggestad J, Halvorson J, Mooney CP, Royce N, Wanta N. On magic type labelings of zero-divisor graphs. IEJA. 2024;36(36):157-83.