University of IsfahanInternational Journal of Group Theory2251-765010220210601On the power graphs of elementary abelian and extra special $p$-groups89952453110.22108/ijgt.2020.120552.1588ENMasoudPourhasanDepartment of Mathematics, Science and Research Branch Islamic Azad University, Tehran, IranHosseinDoostieDepartment of Mathematics, Science and Research Branch Islamic Azad University, Tehran, IranJournal Article20191215For a given odd prime $p$, we investigate the power graphs of three classes of finite groups: the elementary abelian groups of exponent $p$, and the extra special groups of exponents $p$ or $p^2$. We show that these power graphs are Eulerian for every $p$. As a corollary, we describe two classes of non-isomorphic groups with isomorphic power graphs. In addition, we prove that the clique graphs of the power graphs of two considered classes are complete.https://ijgt.ui.ac.ir/article_24531_f2605f3fd1e6973bd072461a34d1e78d.pdf