The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b <=((a - 1)^2)/2 (ii) molecular graphs with m edges and k pendent vertices, if 6 (n^3) -((9m + 2k)n^2) + 4(m^3) >= 0 (iii) triregular graphs of degree 1, a, b that are quadrangle-free, whose average vertex degree exceeds a , that have not more than 12n/13 pendent vertices, if 5<= a < b<=((a - 1)^2)/2 .