Energy of strong double graphs

Let G be a graph of order n with the vertex set V(G) = {v(1) , v(2) , . v(n)}. The strong double graph Sd(G) of a graph G is a graph obtained by taking two copies of G in which a vertex v(i) in one copy is adjacent to a vertex v(j) in the another copy if i = j or v(i) and v(j) are adjacent in G. The energy of a graph G is the sum of the absolute values of its eigenvalues. In this article, an exact relation between the energy of iterated strong double graphs and the energy of a graph together with some other graph parameters is given. Also an exact relation between the energy of extended bipartite double graphs of iterated strong double graphs and the energy of extended bipartite double graphs is given. As a consequence, various energy types are discussed.