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

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 p2. 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