Document Type : Research Paper

**Authors**

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

**Abstract**

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.

**Keywords**

**Main Subjects**

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June 2021

Pages 89-95

**Receive Date:**15 December 2019**Revise Date:**24 March 2020**Accept Date:**25 March 2020**Published Online:**01 June 2021