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On Co-Maximal Subgroup Graph of $D_n$ | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 بهمن 1402 اصل مقاله (431.7 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28396.1528 | ||
| نویسندگان | ||
| Angsuman Das1؛ Manideepa Saha* 2 | ||
| 1Department of Mathematics, Presidency University, Kolkata, India | ||
| 2School of Mathematical Sciences, NISER, Bhubaneshwar, India | ||
| چکیده | ||
| Let $G$ be a group and $S$ be the collection of all non-trivial proper subgroups of $G$. The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is defined to be a graph with $S$ as the set of vertices and two distinct vertices $H$ and $K$ are adjacent if and only if $HK=G$. In this paper, we study the comaximal subgroup graph on finite dihedral groups. In particular, we study order, maximum and minimum degree, diameter, girth, domination number, chromatic number and perfectness of comaximal subgroup graph of dihedral groups. Moreover, we prove some isomorphism results on comaximal subgroup graph of dihedral groups. | ||
| کلیدواژه‌ها | ||
| dihedral group؛ graph isomorphism؛ perfect graph | ||
| مراجع | ||
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[1] S. Akbari, B. Miraftab, and R. Nikandish, Co-maximal graphs of subgroups of groups, Can. Math. Bull. 60 (2017), no. 1, 12–25. https://doi.org/10.4153/CMB-2016-026-0
[2] P.J. Cameron, Graphs defined on groups, Int. J. Group Theory 11 (2022), no. 2, 53–107. https://doi.org/10.22108/ijgt.2021.127679.1681
[3] K. Conrad, Notes on dihedral groups, https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral2.pdf.
[4] A. Das and M. Saha, On co-maximal subgroup graph of a group-II, Ric. Mat., In press. https://doi.org/10.1007/s11587-023-00836-3
[5] A. Das, M. Saha, and S. Al-Kaseasbeh, On co-maximal subgroup graph of a group, Ric. Mat., 73 (2024), 2075–2089. https://doi.org/10.1007/s11587-022-00718-0
[6] B. Miraftab and R. Nikandish, Co-maximal graphs of two generator groups, J. Algebra Appl. 18 (2019), no. 4, Article ID:1950068. https://doi.org/10.1142/S0219498819500683
[7] M. Saha, S. Biswas, and A. Das, On co-maximal subgroup graph of Zn, Int. J. Group Theory 11 (2022), no. 4, 221–228. https://doi.org/10.22108/ijgt.2021.129788.1732 | ||
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