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A Simple-Intersection Graph of a Ring Approach to Solving Coloring Optimization Problems | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 آذر 1402 اصل مقاله (413.73 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28858.1752 | ||
| نویسندگان | ||
| Fida Moh'd؛ Mamoon Ahmed* | ||
| Department of Basic Sciences, Princess Sumaya University for Technology, Amman, Jordan | ||
| چکیده | ||
| In this paper, we introduce a modified version of the simple-intersection graph for semisimple rings, applied to a ring $R$ with unity. The findings from this modified version are subsequently utilized to solve several coloring optimization problems. We demonstrate how the clique number of the simple-intersection graph can be used to determine the maximum number of possibilities that can be selected from a set of $n$ colors without replacement or order, subject to the constraint that any pair shares only one common color. We also show how the domination number can be used to determine the minimum number of possibilities that can be selected, such that any other possibility shares one color with at least one of the selected possibilities, is $n-1$. | ||
| کلیدواژه‌ها | ||
| Simple-intersection graph؛ semisimple rings؛ ideals؛ cliques؛ girth | ||
| مراجع | ||
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[1] S. Akbari and R. Nikandish, Some results on the intersection graph of ideals of matrix algebras, Linear Multilinear Algebra 62 (2014), no. 2, 195–206. https://doi.org/10.1080/03081087.2013.769101 [2] S. Akbari, R. Nikandish, and M.J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl. 12 (2013), no. 4, Article ID: 1250200. https://doi.org/10.1142/S0219498812502003 [3] T. Alraqad, H. Saber, and R. Abu-Dawwas, Intersection graphs of graded ideals of graded rings, AIMS Math. 6 (2021), 10355–10368. https://doi.org/10.3934/math.2021600 [4] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434–447. https://doi.org/10.1006/jabr.1998.7840 [5] N. Ashrafi, H.R. Maimani, M.R. Pournaki, and S. Yassemi, Unit graphs associated with rings, Comm Algebra 38 (2010), no. 8, 2851–2871. https://doi.org/10.1080/00927870903095574 [6] J. A. Bondy and U.S.R. Murty, Graph Theory, Springer-Verlag, London, 2011.
[7] I. Chakrabarty, S. Ghosh, T.K. Mukherjee, and M.K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), no. 17, 5381–5392. https://doi.org/10.1016/j.disc.2008.11.034 [8] I. Chakrabarty and J.V. Kureethara, A survey on the intersection graphs of ideals of rings, Commun. Comb. Optim. 7 (2022), no. 2, 121–167. https://doi.org/10.22049/cco.2021.26990.1176 [9] P.M. Cohn, Introduction to Ring Theory, Springer Science & Business Media, London, 2012.
P. Devi and R. Rajkumar, On the complement of the intersection graph of subgroups of a group, Commun. Comb. Optim., In press. https://doi.org/10.22049/cco.2023.28198.1476 [11] S.H. Jafari and N. Jafari Rad, Planarity of intersection graphs of ideals of rings, Int. Electron. J. Algebra 8 (2010), 161–166.
[12] N. Jafari Rad, S.H. Jafari, and S. Ghosh, On the intersection graphs of ideals of direct product of rings, Discuss. Math. Gen. Algebra Appl. 34 (2014), no. 2, 191–201. http://dx.doi.org/10.7151/dmgaa.1224 [13] A.V. Kelarev, On undirected cayley graphs, Australas. J. Combin. 25 (2002), 73–78.
[14] L.A. Mahdavi and Y. Talebi, Co-intersection graph of submodules of a module, Algebra Discrete Math. 21 (2016), no. 1, 128–143.
[15] H.R. Maimani, M. Salimi, A. Sattari, and S. Yassemi, Comaximal graph of commutative rings, J. Algebra 319 (2008), no. 4, 1801–1808. https://doi.org/10.1016/j.jalgebra.2007.02.003 [16] J. Matczuk and A. Majidinya, Sum-essential graphs of modules, J. Algebra Appl. 20 (2021), no. 11, Article ID: 2150211. https://doi.org/10.1142/S021949882150211X [17] J. Matczuk, M. Nowakowska, and E.R. Puczyłowski, Intersection graphs of modules and rings, J. Algebra Appl. 17 (2018), no. 07, Article ID: 1850131. https://doi.org/10.1142/S0219498818501311 [18] F. Moh’d and M. Ahmed, Simple-intersection graphs of rings, AIMS Math. 8 (2023), no. 1, 1040–1054. https://doi.org/10.3934/math.2023051 [19] E. A. Osba, The intersection graph for finite commutative principal ideal rings, Acta Math. Acad. Paedagog. Nyiregyhaziensis 32 (2016), no. 1, 15–22.
[20] Z.S. Pucanović and Z.Z. Petrović, Toroidality of intersection graphs of ideals of commutative rings, Graphs Combin. 30 (2014), 707–716. https://doi.org/10.1007/s00373-013-1292-1 | ||
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