On Power Graph Representation of Γ_1-nonderanged Permutation Group
DOI:
https://doi.org/10.56919/usci.2541.006Keywords:
Group, permutation group, nonderanged permutation group, power graph, adjacency matrixAbstract
Study’s Excerpt:
- An undirected power graph representation of -nonderanged permutation group has been constructed.
- Ithas been proved that is connected for any and is neither regular nor complete except at
- The adjacency matrix of some selected graphs together with pictorial representations was also
Full Abstract:
A -nonderanged permutation group is a permutation group such that where . In this paper, an undirected power graph representation of -nonderanged permutation group denoted by has been studied. It was proved, among other things, that the graph is connected for any and is neither regular nor complete except at Also, the maximum degree of is and the girth is three (3) for any while the diameter is one (1) for and two (2) for. Furthermore, the central vertex of the graph was proved to be for any and while the peripheral vertex is for p > 5. Lastly, the adjacency matrix of some selected graphs and their graphical representations were given to support our findings.
References
Adeniran, J. O., Akinmoyewa, Solarin, A. R. T., and Jaiyeola, T. G. (2011). On some Algebraic Properties of Generalized Groups. Acta Mathematica Academaiae Paedagogicae Nyiregyhaziensis, 27, 23-30.
Beaumont, R. A., and Peterson, R. P. (1955). Set-Transitive Permutation Groups, Cambridge University Press. https://doi.org/10.4153/CJM-1955-005
Calkin, N. J., Canfield, E. R., and Wilf, H. S. (2000). Averaging Sequences, Deranged Mappings, and a Problem of Lampert and Slater. Journal of Combinatorial Theory, Series A, 91, 171-190. https://doi.org/10.1006/jcta.2000.3093
Chakrabarty, I., Ghosh, S., and Sen, M. K. (2009). Undirected power graphs of semigroups. In Semigroup Forum (Vol. 78, pp. 410-426). Springer-Verlag. https://doi.org/10.1007/s00233-008-9132-y
Chelvam, T. T., and Sattanathan, M. (2013). Power graph of finite Abelian groups. Algebra and Discrete Mathematics, 16(1).
Dixon, J. D., and Mortimer, B. (1996). Graduate Texts in Mathematics, Permutation Groups, (163). https://doi.org/10.1007/978-1-4612-0731-3
Garba, A. I, Ejima, O., Aremu, K. O., & Usman H. (2017). Nonstandard Young Tableaux of Γ1 Non deranged Permutation Group. Global Journal of Mathematical Analysis, 5(1) 21-23.
Garba, A.I., Yusuf, A., and Hassan, A. (2018). Some Topological Properties of a Constructed Algebraic Structure. Journal of the Nigerian Association of Mathematical Physics,45, 21-26.
Grigorchuk, R., and Medynets, K. (2011). On Algebraic Properties of Topological Full Groups. Russian Academy of Science Sbornik Mathematics, 205(6). https://doi.org/10.1070/SM2014v205n06ABEH004400
Ibrahim A. A., Ejima O., and Aremu K. O. (2016). On the Representations of Γ1-Non deranged Permutation Group. Advances in Pure Mathematics, 6, 608-614. https://doi.org/10.4236/apm.2016.69049
Ibrahim A., Ibrahim M., and Ibrahim, B. A. (2022). Embracing Sum using Ascent Block of Γ1 Non deranged Permutation Group. International Journal of Advances in Engineering and Management, 4(5). https://doi.org/10.35629/5252-0405272277
Kelarev, A. V., & Quinn, S. J. (2002). Directed graphs and combinatorial properties of semigroups. Journal of Algebra, 251(1), 16-26. https://doi.org/10.1006/jabr.2001.9128
Suleiman, Garba, A. I., and Mustapha, A. (2020). On some Non-deranged permutation: A new method of Construction, International Journal of Research - GRANTHAALAYAH, 8(3). https://doi.org/10.29121/granthaalayah.v8.i3.2020.162
Yusuf, A., & Ejima, O. (2023). Some Properties of an extended Γ1-non deranged permutation group. Fudma Journal of Sciences, 7(3), 332-336. https://doi.org/10.33003/fjs-2023-0703-2031
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