University of Isfahan International Journal of Group Theory 2251-7650 10 2 2021 06 01 On the power graphs of elementary abelian and extra special $p$-groups‎ 89 95 24531 10.22108/ijgt.2020.120552.1588 EN Masoud Pourhasan Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran Hossein Doostie Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran Journal Article 2019 12 15 ‎For 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