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Commutative rings introduce a class of identifiable graphs | ||
Transactions on Combinatorics | ||
مقاله 2، دوره 14، شماره 2، شهریور 2025، صفحه 79-88 اصل مقاله (471.89 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2024.138005.2081 | ||
نویسندگان | ||
Reza Nikandish* ؛ Asma Korehpaz؛ Omid Khaninasab | ||
Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran | ||
چکیده | ||
Let $R$ be a commutative ring with identity, and $ \mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ \mathrm{A}(R)^{*}=\mathrm{A}(R)\setminus\lbrace 0\rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, we characterize all positive integers $n$ for which $AG(\mathbb{Z}_n)$ is identifiable. | ||
کلیدواژهها | ||
Annihilating-ideal graph؛ Identifying code؛ Identifiable graph | ||
مراجع | ||
[1] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shaveisi, On the coloring of the annihilatingideal graph of a commutative ring, Discrete Math., 312 no. 17 (2012) 2620–2626. [13] M. G. Karpovsky, K. Chakrabarty and L. B. Levitin, On a new class of codes for identifying vertices in graphs, IEEE Trans. Inform. Theory, 44 no. 2 (1998) 599–611. | ||
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