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Hypergraphs defined on algebraic structures | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 11، شماره 1، خرداد 2026، صفحه 131-144 اصل مقاله (480.77 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29607.2077 | ||
| نویسندگان | ||
| Peter J. Cameron1؛ Aparna Lakshmanan S2؛ Midhuna V. Ajith* 2 | ||
| 1School of Mathematics and Statistics University of St. Andrews Fife, UK | ||
| 2Department of Mathematics Cochin University of Science and Technology, Cochin - 22 Kerala, India | ||
| چکیده | ||
| There has been a great deal of research on graphs defined on algebraic structures in the last two decades. Power graphs, commuting graphs, cyclic graphs are some examples. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. | ||
| کلیدواژهها | ||
| commuting hypergraphs؛ power hypergraphs؛ enhanced power hypergraphs؛ generating hypergraphs | ||
| مراجع | ||
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[1] G. Aalipour, S. Akbari, P. J. Cameron, R. Nikandish, and F. Shaveisi, On the structure of the power graph and the enhanced power graph of a group, Electron. J. Comb. 24 (2017), no. 3, #P3.16.
[2] I. Chakrabarty, S. Ghosh, and M. K. Sen, Undirected power graphs of semigroups, Semigroup Forum 78 (2009), no. 3, 410–426. https://doi.org/10.1007/s00233-008-9132-y
[3] R. Dharmarajan and K. Kannan, Hyper paths and hyper cycles, Int. J. Pure Appl. Math 98 (2015), no. 3, 309–312. http://dx.doi.org/10.12732/ijpam.v98i3.2 [4] S.D. Freedman, A. Lucchini, D. Nemmi, and C.M. Roney-Dougal, Finite groups satisfying the independence property, Internat. J. Algebra Comput. 33 (2023), no. 3, 509–545. https://doi.org/10.1142/S021819672350025X
[5] A. Lucchini, The independence graph of a finite group, Monatsh. fur Math. 193 (2020), no. 4, 845–856. https://doi.org/10.1007/s00605-020-01445-0
[6] J.G. Oxley, Matroid Theory, Oxford University Press, USA, 1992.
[7] V.I. Voloshin, Introduction to Graph and Hypergraph Theory, Nova Science Publishers, New York, 2009. | ||
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