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On the unitary Cayley graphs of group rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، S1، تیر 2026، صفحه 247-255 اصل مقاله (163.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.28297.1705 | ||
| نویسندگان | ||
| K. Limkul؛ S. Nanta* | ||
| Department of Applied Mathematics and Statistics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun, Thailand | ||
| چکیده | ||
| Let $R$ be a ring. The unitary Cayley graph of a ring $R$, denoted by $\Gamma(R)$, is a graph with vertex set $R$ where two vertices $u,v\in R$ are adjacent if and only if $u-v$ is a unit of $R$. In this paper, we investigate the unitary Cayley graph of a finite ring, called a group ring, and examine its fundamental properties. We present the conditions for adjacency, the connectivity of the graph and its basic structure. Additionally, we provide the exact value of the degree of a vertex and the distance between any two vertices within the graph. | ||
| کلیدواژهها | ||
| Unitary Cayley graph؛ Group ring؛ Connectivity؛ Distance | ||
| مراجع | ||
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[1] R. Akhtar, M. Boggess, T. Jackson-Henderson, I. Jiménez, R. Karpman, A. Kinzel and D. Pritikin, On the unitary Cayley graph of a finite ring, Electron. J. Combin., 16 (2009). [2] I. Beck, Coloring of commutative rings, J. Algebra, (1) 116 (1988), 208–226. [3] A. Cayley, VII. On the theory of groups, as depending on the symbolic equation θn = 1, Lond. Edinb. Dubl. Phil. Mag., 7 (1854), 40–47. [4] Q. Cheng, J. Zhang and J. Zhuang, LWE from non-commutative group rings, Des. Codes Cryptogr., 90 (2022), 239–263. [5] I. Dejter and R. E. Giudici, On unitary Cayley graphs, Combin. Math. Combin. Comput., 18 (1995), 121–124. [6] R. Diestel, Graph theory (graduate texts in mathematics), Springer, 2005. [7] S. T. Dougherty, J. Gildea, A. Korban and A. Kaya, Composite matrices from group rings, composite G-codes and constructions of self-dual codes, Des. Codes Cryptogr., 89 (2005), 1615–1638. [8] A. Ilic, The energy of unitary Cayley graphs, Linear Algebra Appl., 431 (2009), 1881–1889. [9] E. Noether, Hypercomplexe grössen and darstellungtheorie, Math. Z., 30 (1929), 641–692. [10] D. Kiani and M. M. Haji Aghaei, On the unitary Cayley graph of a ring, Electron. J. Combin., (2) 19 (2012). [11] D. Kiani and M.M. Haji Aghaei, On the unitary Cayley graphs of matrix algebras, Linear Algebra Appl., 466 (2015), 421–428. [12] W. Klotz and T. Sander, Some properties of unitary Cayley graphs, Electron. J. Combin., 14 (2007). [13] S. Kumar, G. Mittal and S. Kumar, Digital signature schemes based on group ring, SN Comput. Sci., 3 (2022). [14] X. Liu and B. Li, Distance powers of unitary Cayley graphs, Appl. Math. Comput., 289 (2016), 272-280. [15] C. P. Milies and S. K. Sehgal, An introduction to group rings, Kluwer Academic Publishers, Netherlands, 2002. | ||
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