On the power graphs of elementary abelian and extra special $p$-groups‎

Document Type : Research Paper


Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran


‎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.


Main Subjects

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