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Rahbariyan, Sakineh. (1403). On the tree-number of the power graph associated with some finite groups. نشریه مهندسی عمران امیرکبیر, 5(2), 81-89. doi: 10.22060/ajmc.2023.21910.1123
Sakineh Rahbariyan. "On the tree-number of the power graph associated with some finite groups". نشریه مهندسی عمران امیرکبیر, 5, 2, 1403, 81-89. doi: 10.22060/ajmc.2023.21910.1123
Rahbariyan, Sakineh. (1403). 'On the tree-number of the power graph associated with some finite groups', نشریه مهندسی عمران امیرکبیر, 5(2), pp. 81-89. doi: 10.22060/ajmc.2023.21910.1123
Rahbariyan, Sakineh. On the tree-number of the power graph associated with some finite groups. نشریه مهندسی عمران امیرکبیر, 1403; 5(2): 81-89. doi: 10.22060/ajmc.2023.21910.1123

On the tree-number of the power graph associated with some finite groups

AUT Journal of Mathematics and Computing
مقاله 1، دوره 5، شماره 2، 2024، صفحه 81-89    اصل مقاله (409.29 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2023.21910.1123
نویسنده
Sakineh Rahbariyan*
Department of Mathematics, Faculty of Sciences, Arak University, Arak, Iran
چکیده
Given a group $G$, we define the power graph $\mathcal{P}(G)$ as follows: the vertices are the elements of $G$ and two vertices $x$ and $y$ are joined by an edge if $\langle x \rangle \subseteq \langle y \rangle$ or $\langle y \rangle \subseteq \langle x \rangle$. Obviously the power graph of any group is always connected, because the identity element of the group is adjacent to all other vertices. We consider $\kappa(G)$, the number of spanning trees of the power graph associated with a finite group $G$. In this paper, for a finite group $G$, first we represent some properties of $\mathcal{P}(G)$, then we are going to find some divisors of $\kappa(G)$, and finally we prove that the simple group $A_6\cong L_2(9)$ is uniquely determined by tree-number of its power graph among all finite simple groups.
کلیدواژه‌ها
Power graph؛ Tree-number؛ Simple group
مراجع
  1. Abawajy, A. Kelarev, and M. Chowdhury, Power graphs: a survey, Electron. J. Graph Theory Appl. (EJGTA), 1 (2013), pp. 125–147.
  2. Biggs, Algebraic graph theory, Cambridge Mathematical Library, Cambridge University Press, Cambridge, second ed., 1993.
  3. J. Cameron, The power graph of a finite group, II, J. Group Theory, 13 (2010), pp. 779–783.
  4. Cayley, A theorem on trees., Quart. J., 23 (1888), pp. 376–378.
  5. Chakrabarty, S. Ghosh, and M. K. Sen, Undirected power graphs of semigroups, Semigroup Forum, 78 (2009), pp. 410–426.
  6. Y. Chen, A. R. Moghaddamfar, and M. Zohourattar, Some properties of various graphs associated with finite groups, Algebra Discrete Math., 31 (2021), pp. 195–211.
  7. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.
  8. Kelarev, Graph algebras and automata, vol. 257 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 2003.
  9. Kelarev, J. Ryan, and J. Yearwood, Cayley graphs as classifiers for data mining: the influence of asymmetries, Discrete Math., 309 (2009), pp. 5360–5369.
  10. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of groups, in Contributions to general algebra, 12 (Vienna, 1999), Heyn, Klagenfurt, 2000, pp. 229–235.
  11. Kirkland, A. R. Moghaddamfar, S. Navid Salehy, S. Nima Salehy, and M. Zohourattar, The complexity of power graphs associated with finite groups, Contrib. Discrete Math., 13 (2018), pp. 124–136.
  12. R. Moghaddamfar, S. Rahbariyan, S. Navid Salehy, and S. Nima Salehy, The number of spanning trees of power graphs associated with specific groups and some applications, Ars Combin., 133 (2017), pp. 269– 296.
  13. R. Moghaddamfar, S. Rahbariyan, and W. J. Shi, Certain properties of the power graph associated with a finite group, J. Algebra Appl., 13 (2014), p. 1450040, 18.
  14. S. Rose, A course on group theory, Cambridge University Press, Cambridge-New York-Melbourne, 1978.
  15. N. V. Temperley, On the mutual cancellation of cluster integrals in Mayer’s fugacity series, Proc. Phys. Soc., 83 (1964), pp. 3–16.
  16. B. West, Introduction to graph theory, Prentice Hall, Inc., Upper Saddle River, NJ, second ed., 2001.
  17. V. Zavarnitsine, Finite simple groups with narrow prime spectrum, Sib. Elektron. Mat. Izv., 6 (2009),` pp. 1–12.
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