全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用：99美元
投递稿件

查看量下载量

相关文章

更多...

一些环的Nil-Clean图的导出子图中的完备码
Perfect Codes in Induced Subgraphs of Nil-Clean Graphs for Some Rings

DOI: 10.12677/pm.2026.161014, PP. 112-121

Keywords: Nil-Clean图，导出子图，完备码
Nil-Clean Graphs, Induced Subgraph, Perfect Codes

Full-Text   Cite this paper   Add to My Lib

Abstract:

设 R 是一个环。如果一个元素 r∈R 可以分解成 R 中的一个幂等元与一个幂零元的和，那么就称 r 为 R 中的一个nil-clean元。 R 的nil-clean图记为 G NC ( R ) ，其点集为 R ，两个不同的点 x 和 y 是邻接的当且仅当 x+y 是 R 中的一个nil-clean元。设 G 是一个有限无向简单图，其点集为 V( G ) 。设 C 是 V( G ) 的一个非空子集。如果当 c i 取遍 C 中所有元素时， c i 的半径为1的闭邻域 S 1 ( c i ) 构成 V( G ) 的一个划分，则称 C 为图

References

[1]  Biggs, N. (1973) Perfect Codes in Graphs. Journal of Combinatorial Theory, Series B, 15, 289-296.
https://doi.org/10.1016/0095-8956(73)90042-7
[2]  Mudaber, M.H., Sarmin, N.H. and Gambo, I. (2021) Perfect Codes over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo N. Wseas Transactions on Mathematics, 20, 399-403.
https://doi.org/10.37394/23206.2021.20.41
[3]  Mudaber, M.H., Sarmin, N.H. and Gambo, I. (2022) Perfect Codes in Spanning Subgraphs of Unit Graphs Associated with Some Boolean Rings. Proceedings of Science and Mathematics, 6, 86-89.
[4]  Mudaber, M.H., Sarmin, N.H. and Gambo, I. (2022) Perfect Codes in Unit Graph of Some Commutative Rings. Ad-vances and Applications in Mathematical Sciences, 21, 1895-1905.
[5]  Mudaber, M.H., Sarmin, N.H. and Gambo, I. (2022) Perfect Codes in Induced Subgraph of Unit Graph Associated with Some Commutative Rings. Jurnal Teknologi, 84, 131-136.
https://doi.org/10.11113/jurnalteknologi.v84.17982
[6]  Mudaber, M.H., Sarmin, N.H. and Gambo, I. (2024) Perfect Codes in Unity Product Graph of Some Commutative Rings. Southeast Asian Bulletin of Mathematics, 48, 401-409.
[7]  Ma, X., Zhong, G. and Wang, K. (2023) Perfect Codes in Commuting Graphs of Symmetric Groups. Acta Mathe-Matica Sinica Chinese Series, 66, 475-484.
[8]  Huo, L., Yi, G. and Li, M. (2025) Perfect Codes in Commuting Graphs on Several Finite Non-Abelian Groups. Journal of Mathematics, 45,429-434.
[9]  Lint, J.H.V. (1975) A Survey of Perfect Codes. Rocky Mountain Journal of Mathematics, 5, 199-224.
https://doi.org/10.1216/rmj-1975-5-2-199
http://www.jstor.org/stable/44236426
[10]  Diesl, A.J. (2013) Nil Clean Rings. Journal of Algebra, 383, 197-211.
https://doi.org/10.1016/j.jalgebra.2013.02.020
[11]  Basnet, D.K. and Bhattacharyya, J. (2017) Nil Clean Graphs of Rings. Algebra Colloquium, 24, 481-492.
https://doi.org/10.1142/s1005386717000311
[12]  Chartrand, G. and Zhang, P. (2013) A First Course in Graph Theory. Dover Publications.
[13]  Evans, A.B., Fricke, G.H., Maneri, C.C., McKee, T.A. and Perkel, M. (1994) Representations of Graphs Modulo n. Journal of Graph Theory, 18, 801-815.
https://doi.org/10.1002/jgt.3190180805

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133