Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24494120230201A new characterization of some characteristically simple groups9197486410.22060/ajmc.2022.21283.1083ENZohrehSayanjaliDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran0000-0003-1189-951XJournal Article20220413Let $G$ be a finite group and $\mathrm{cd}(G)$ be the set of irreducible complex character degrees of $G$. It was proved that some finite simple groups are uniquely determined by their orders and their degree graphs. Recently, in [Behravesh, et al., Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph, Int. J. Group Theory, DOI: 10.22108/ijgt.2019.113029.1502.] new characterizations for some finite simple groups are given. Also, in [Qin, et al., Mathieu groups and its degree prime-power graphs, Comm. Algebra, 2019] the degree prime-power graph of a finite group is introduced and it is proved that the Mathieu groups are uniquely determined by order and degree prime-power graph. In this paper we continue this work and we characterize some simple groups and some characteristically simple groups by their orders and some vertices of their degree prime-power graphs.https://ajmc.aut.ac.ir/article_4864_c466f2fa6e86b0481f688edf99b8852a.pdf