  For a graph $G$ with vertex set $V(G)=\{v_1, v_2, \cdots, v_n\}$, the
extended double cover $G^*$ is a bipartite graph with bipartition (X, Y),
$X=\{x_1, x_2, \cdots, x_n\}$ and $Y=\{y_1, y_2, \cdots, y_n\}$, where two
vertices $x_i$ and $y_j$ are adjacent if and only if $i=j$ or $v_i$ adjacent to
$v_j$ 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 neighbours 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 $G^{k*}$ 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.
