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On prime coprime graphs of certain finite groups | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 شهریور 1405 اصل مقاله (486.08 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30921.2661 | ||
| نویسندگان | ||
| Ravi Ranjan؛ Shubh N. Singh* | ||
| Department of Mathematics, Central University of South Bihar, Gaya–824236, Bihar, India | ||
| چکیده | ||
| The prime coprime graph $\Theta(G)$ of a finite group $G$ is the graph whose vertex set is $G$ and any two distinct vertices are adjacent if the greatest common divisor of their orders is either $1$ or a prime. In this paper, we investigate Hamiltonicity, clique number, and vertex degree of $\Theta(G)$ for cyclic, dihedral, and dicyclic groups $G$. We establish that $\Theta(G)$ admits a $(k,1)$-partition for cyclic, dihedral, and dicyclic groups $G$ of specified orders. | ||
| کلیدواژهها | ||
| Hamiltonian graph؛ clique number؛ H-join؛ (k؛ l)-partition | ||
| مراجع | ||
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[1] A. Adhikari and S. Banerjee, Prime coprime graph of a finite group, Novi Sad J. Math. 52 (2022), no. 2, 41–59.
[2] A. Brandstädt, Partitions of graphs into one or two independent sets and cliques, Discrete Math. 152 (1996), no. 1-3, 47–54. https://doi.org/10.1016/0012-365X(94)00296-U
[3] D.M. Burton, Elementary Number Theory, 6th ed., McGraw-Hill, New York, 2007.
[4] 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
[5] D.M. Cardoso, M.A. de Freitas, E.A. Martins, and M. Robbiano, Spectra of graphs obtained by a generalization of the join graph operation, Discrete Math. 313 (2013), no. 5, 733–741. https://doi.org/10.1016/j.disc.2012.10.016
[6] M.W. Ecker, When does a sum of positive integers equal their product?, Math. Mag. 75 (2002), no. 1, 41–47. https://doi.org/10.2307/3219187 [7] S. Foldes and P.L. Hammer, Split graphs having Dilworth number two, Canad. J. Math. 29 (1977), no. 3, 666–672. https://doi.org/10.4153/CJM-1977-069-1 [8] J.A. Gallian, Contemporary Abstract Algebra, 10th ed., Chapman and Hall/CRC, New York, 2021.
[9] S. Hao, G. Zhong, and X. Ma, Notes on the co-prime order graph of a group, vol. 75, 2022, pp. 340–348.
[10] G. James and M. Liebeck, Representations and Characters of Groups, 2nd ed., Cambridge University Press, New York, 2001.
[11] H. Li, G. Zhong, and X. Ma, Finite groups whose co-prime order graphs have positive genus, Proceedings of the Bulgarian Academy of Sciences 75 (2022), no. 9, 1270–1278. https://doi.org/10.7546/CRABS.2022.09.03
[12] R. Ranjan and S.N. Singh, An inequality for Euler’s phi-function, Manuscript, 2025.
[13] M. Saini, S.M.S. Khasraw, A. Sehgal, and D. Singh, On co-prime order graphs of finite abelian p-groups, J. Math. Comput. Sci. 11 (2021), no. 6, 7052–7061.
[14] M. Saini, V. Kumari, P. Rana, A. Sehgal, and D. Singh, Degree based matrices of co-prime order graph of finite groups, Math. Stat. 13 (2025), no. 3, 127–135. https://doi.org/10.13189/ms.2025.130301
[15] M. Saini, G. Singh, A. Sehgal, and D. Singh, On divisor labeling of co-prime order graphs of finite groups, Italian J. Pure Appl. Math. 51 (2024), no. 3, 443–451.
[16] M. Sattanathan and R. Kala, An introduction to order prime graph, Int. J. Contemp. Math. Sciences 4 (2009), no. 10, 467–474.
[17] A.J. Schwenk, Computing the characteristic polynomial of a graph, Graphs and Combinatorics, Lecture Notes in Mathematics, vol. 406, Springer-Verlag, Berlin, 1974, pp. 153–172. https://doi.org/10.1007/BFb0066438
[18] A. Sehgal, S. Manjeet, and D. Singh, Co-prime order graphs of finite abelian groups and dihedral groups, J. Math. Comput. Sci. 23 (2021), no. 3, 196–202. https://doi.org/10.22436/jmcs.023.03.03
[19] D.B. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, Upper Saddle River, 2001. | ||
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آمار تعداد مشاهده مقاله: 52 تعداد دریافت فایل اصل مقاله: 59 |
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