arXiv subjects
Publications and source records attributed to Alireza Doostabadi.
We determine the diameter of every connected component of the complement of the power graph and the enhanced power graph of a finite group, which completely answers two questions by Peter J. Cameron.
The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the other. Various kinds of planarity of (proper) power graphs of groups are discussed.
The power graph $\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\in\langle y\rangle$ or $y\in\langle x\rangle$. We characterize all finite groups $G$ whose power graphs are claw-free, $K_{1,4}$-free or $C_4$-free.
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.