Energy, Laplacian energy of double graphs and new families of equienergetic graphs

For a graph G with vertex set V(G) = {v(1), v(2),..., v(n)}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x(1), x(2),..., x(n)} and Y = {y(1), y(2),..., y(n)}, where two vertices x(i) and y(j) are adjacent if and only if i = j or vi adjacent to v(i) in G. The double graph D[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the neighbors of corresponding vertex in another copy. In this paper we study energy and Laplacian energy of the graphs G* and D[ G], L-spectra of Gk* the k-th iterated extended double cover of G. We obtain a formula for the number of spanning trees of G*. We also obtain some new families of equienergetic and L-equienergetic graphs.