آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 117 |
| تعداد مقالات | 1,391 |
| تعداد مشاهده مقاله | 1,409,419 |
| تعداد دریافت فایل اصل مقاله | 1,376,540 |
Line graph characterization of the order supergraph of a finite group | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 مرداد 1403 اصل مقاله (543.39 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29375.1962 | ||
| نویسندگان | ||
| M. Manisha؛ P. Parveen؛ Jitender Kumar* | ||
| Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani-333031, India | ||
| چکیده | ||
| The power graph ${\mathcal{P}(G)}$ is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. The order supergraph ${\mathcal{S}(G)}$ of the power graph ${\mathcal{P}(G)}$ is the simple undirected graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if $o(x)\vert o(y)$ or $o(y)\vert o(x)$. In this paper, we classify all the finite groups $G$ such that the order supergraph ${\mathcal{S}(G)}$ is the line graph of some graph. Moreover, we characterize finite groups whose order supergraphs are the complement of line graphs. | ||
| کلیدواژه‌ها | ||
| Power graph؛ order supergraph of power graph؛ line graph؛ finite groups؛ EPPO-group | ||
| مراجع | ||
|
[1] Z. Barati, Line zero divisor graphs, J. Algebra Appl. 20 (2021), no. 9, Article ID: 2150154. https://doi.org/10.1142/S0219498821501541
[2] L.W. Beineke, Characterizations of derived graphs, J. Combin. Theory 9 (1970), no. 2, 129–135. https://doi.org/10.1016/S0021-9800(70)80019-9
[3] S. Bera, Line graph characterization of power graphs of finite nilpotent groups, Comm. Algebra 50 (2022), no. 11, 4652–4668. https://doi.org/10.1080/00927872.2022.2069793
[4] P.J. Cameron, The power graph of a finite group, II, J. Group Theory 13 (2010), no. 6, 779–783. https://doi.org/10.1515/jgt.2010.023
[5] P.J. Cameron and S. Ghosh, The power graph of a finite group, Discrete Math. 311 (2011), no. 13, 1220–1222. https://doi.org/10.1016/j.disc.2010.02.011
[6] A. Doostabadi, A. Erfanian, and D.G. Farrokhi, On power graphs of finite groups with forbidden induced subgraphs, Indag. Math. 25 (2014), no. 3, 525–533. https://doi.org/10.1016/j.indag.2014.01.003
[7] D.S. Dummit and R.M. Foote, Abstract Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991.
[8] A. Hamzeh and A.R. Ashrafi, Automorphism groups of supergraphs of the power graph of a finite group, European J. Combin. 60 (2017), 82–88. https://doi.org/10.1016/j.ejc.2016.09.005
[9] A. Hamzeh and A.R. Ashrafi, The order supergraph of the power graph of a finite group, Turkish J. Math. 42 (2018), no. 4, 1978–1989. https://doi.org/10.3906/mat-1711-78
[10] A. Hamzeh and A.R. Ashrafi, Some remarks on the order supergraph of the power graph of a finite group, Int. Electron. J. Algebra 26 (2019), 1–12. https://doi.org/10.24330/ieja.586838
[11] A. Kelarev, Graph Algebras and Automata, CRC Press, New York, 2003.
[12] A. Kelarev, Labelled Cayley graphs and minimal automata, Australas. J. Combin. 30 (2004), 95–101.
[13] A. Kelarev, J. Ryan, and J. Yearwood, Cayley graphs as classifiers for data mining: The influence of asymmetries, Discrete Math. 309 (2009), no. 17, 5360–5369. https://doi.org/10.1016/j.disc.2008.11.030
[14] A.V. Kelarev and S.J. Quinn, A combinatorial property and power graphs of groups, Contributions to General Algebra 12 (2000), no. 58, 3–6.
[15] A. Khalili Asboei and S.S.S. Amiri, The main supergraph of finite groups, New York J. Math. 28 (2022), no. 28, 1057–1063.
[16] A. Kumar, L. Selvaganesh, P.J. Cameron, and T.T. Chelvam, Recent developments on the power graph of finite groups–a survey, AKCE Int. J. Graphs Comb. 18 (2021), no. 2, 65–94. https://doi.org/10.1080/09728600.2021.1953359
[17] X. Ma and H. Su, On the order supergraph of the power graph of a finite group, Ric. Mat. 71 (2022), no. 2, 381–390. https://doi.org/10.1007/s11587-020-00520-w [18] P. Manna, P.J. Cameron, and R. Mehatari, Forbidden subgraphs of power graphs, Electron. J. Combin. 28 (2021), no. 3, ♯P3.4 https://doi.org/10.37236/9961
[19] Parveen and J. Kumar, On finite groups whose power graphs are line graphs, J. Algebra Appl. (2024), In press. https://doi.org/10.1142/S0219498825502858 | ||
|
آمار تعداد مشاهده مقاله: 348 تعداد دریافت فایل اصل مقاله: 382 |
||