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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
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