پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 42 |
| تعداد شماره‌ها | 1,510 |
| تعداد مقالات | 12,457 |
| تعداد مشاهده مقاله | 24,683,652 |
| تعداد دریافت فایل اصل مقاله | 10,421,675 |
On the power graphs of elementary abelian and extra special $p$-groups | ||
| International Journal of Group Theory | ||
| مقاله 11، دوره 10، شماره 2، شهریور 2021، صفحه 89-95 اصل مقاله (197.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.120552.1588 | ||
| نویسندگان | ||
| Masoud Pourhasan؛ Hossein Doostie* | ||
| Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran | ||
| چکیده | ||
| For a given odd prime $p$, we investigate the power graphs of three classes of finite groups: the elementary abelian groups of exponent $p$, and the extra special groups of exponents $p$ or $p^2$. We show that these power graphs are Eulerian for every $p$. As a corollary, we describe two classes of non-isomorphic groups with isomorphic power graphs. In addition, we prove that the clique graphs of the power graphs of two considered classes are complete. | ||
| کلیدواژه‌ها | ||
| Power graphs؛ non-group semigroups؛ semidirect product | ||
| مراجع | ||
|
[1] J. Abawajy, A. V. Kelarev and M. Chowdhury, Power graphs: a survey, Electronic J. Graph Theory and Applications, 1 (2013) 125–147. [2] M. Akbari and A. Moghaddamfar, Groups for which the noncommuting graph is a split graph, Int. J. Group Theory, 6 no. 1 (2017) 29–35. [3] A. R. Ashrafi and B. Soleimani, Normal edge-transitive and 12-arc-transitive Cayley graphs on non-abelian groups of order 2pq, p > q are odd primes, Int. J. Group Theory, 3 no. 5 (2016) 1–8. [4] P. J. Cameron, The power graph of a finite group II, J. Group Theory, 13 (2010) 779–783.
[5] P. J. Cameron and S. Ghosh, The power graph of a finite group, Discrete Math., 311 (2011) 1220–1222.
[6] I. Chakrabarty, S. Ghosh and M. K. Sen, Undirected power graphs of semigroups, Semigroup Forum., 78 (2009) 410–426. [7] T. T. Chelvam and M. Sattanathan, Power graphs of finite abelian groups, Algebra and Discrete math., 16 (2013) 33–41. [8] H. R. Dorbidi, A note on the coprime graph of a group, Int. J. Group Theory, 5 no.4 (2016) 17–22.
[9] R. Hafezieh, On nonsolvable groups whose prime degree graphs have four vertices and one triangle, Int. J. Group Theory, 6 no. 3 (2017) 1–6. [10] R. Hafezieh, Bipartite divisor graph for the set of irreducible character degrees, Int. J. Group Theory, 6 no. 4 (2017) 41–51. [11] D. L. Johnson, Presentation of groups, Second Ed, London Math. Soc. Student Texts, Cambridge University Press, Cambridge, 1997. [12] A. Kelarev, J. Ryan and J. Yearwood, Cayley graphs as classifiers for data mining: the influence of asymmetries, Discrete Math., 309 (2009) 5360–5369. [13] A. V. Kelarev, Ring constructions and applications, World Scientific, NJ, 2002.
[14] A. V. Kelarev, Graph algebras and automata, M. Dekker, New York, 2003.
[15] A. Mehranian, A. R. Gholami and A. Ashrafi, Note on the power graph of a finite group, Int. J. Group Theory, 5 no. 1 (2016) 1–10. [16] S. A. Moosavi, On bipartite divisor graph for character degrees, Int. J. Group Theory, 6 no. 1 (2017) 1–7.
[17] G. B. Preston, Semidirect product of semigroups, Proc. Royal Soc. Edinburgh, 102 (A) (1986) 91–102.
[18] E. F. Robertson and Y. Unl¨u, On semigroup presentations, ¨ Proc. Edinburg Math. Soc., 36 (1992) 55–68.
[19] M. Shaker and M. A. Iranmanesh, On groups with specified quotient power graphs, Int. J. Group Theory, 5 (2016) 49–60. [20] T. Tamura, Examples of direct product of semigroups or groupoids, Notices of the American Math. Soc., 8 (1961) 419–422. | ||
|
آمار تعداد مشاهده مقاله: 315 تعداد دریافت فایل اصل مقاله: 423 |
||