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Studying the A4-Graphs for elements of order 3 in tits group T and Mathieu group M20 | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1855-1860 اصل مقاله (401.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5321 | ||
| نویسندگان | ||
| Zainab Hasan Msheree* 1؛ Mohammed Mukheef Abed1؛ Wissam Fadhel Abid2 | ||
| 1Middle Technical University, Technical Instructors Training Institute, Iraq | ||
| 2Middle Technical University, Institute of Technology, Baghdad, Iraq | ||
| تاریخ دریافت: 18 اسفند 1399، تاریخ بازنگری: 06 تیر 1400، تاریخ پذیرش: 12 تیر 1400 | ||
| چکیده | ||
| Assume that $X$ is a subset of the finite group $G$. The A4-graph is known as a simple graph denoted by $ \mathcal{A}_4 (G, X) $ having $X$ as a vertex set and two vertices $ x, y \in X,$ is linked by an edges if $ x\neq y $ and $ {xy}^{-1} = {yx}^{-1} $. In this paper, we consider $ \mathcal{A}_4 (G, X) $ when $G$ is either Tits group T or Mathieu group $M_{20}$ and $X$ is $G$-conjugacy class of elements of order three. Valuable results reached, for example, disc structure, girth, clique number, and diameters of the A4-graph. | ||
| کلیدواژه‌ها | ||
| Finite simple groups؛ A4-graph؛ connectivity؛ cliques | ||
| مراجع | ||
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[1] A. Aubad, S. kadem, and A. H. Majeed,The non-zero divisor graph of a ring, IJPAM. 43 (2020) 975–983. [2] C. Cedillo, R. MacKinney-Romero, M.A. Pizaa, I.A. Robles and R. Villarroel-Flores, Yet Another Graph System, Yags, Version 0.0.5., 2020. [3] H. Conway, R. T. Curtis, S. P. Norton and R. A. Parker, Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford Clarendon Press, 1985. [4] A. Maksimenko and A. Mamontov, The local finiteness of some groups generated by a conjugacy class of order 3 elements, Siberian Math. J. 3 (2007) 508–518. [5] S. M. Kasim and A. Nawawi, On diameter of subgraphs of commuting graph in symplectic group for elements of order three, Sains Malays. 2 (2021) 549–557. [6] J. Tripp, I. Suleiman, S. Rogers R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray, A. Wilson and P. Walsh, A World Wide Web Atlas of Group Representations, 2021. [7] The GAP Group, GAP Groups, Algorithms, and Programming, Version 4.11.1, 2021. | ||
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