The energy of a digraph D is defined as E(D) = ?n,i=1 ?Re(zi)?, where z1, z2, ..., zn are the (possibly complex) eigenvalues of D . We show that if D is a strongly connected digraph on n vertices, a arcs, and c2 closed walks of length two, such that Re(z1) ? (a + c2)=(2n) ? 1 , then E(D) ? n(1 + ?n)=2. Equality holds if and only if D is a directed strongly regular graph with parameters (n, n+?n/2, 3n+2?n/8, n+2?n/8, n+2?n/8). This bound extends to digraphs an earlier result [J. H. Koolen, V. Moulton:, Maximal energy graphs. Adv. Appl. Math., 26 (2001), 47-52], obtained for simple graphs.

We obtain lower and upper bounds on general multiplicative Zagreb indices for graphs of given clique number and order. Bounds on the basic multiplicative Zagreb indices and on the multiplicative sum Zagreb index follow from our results. We also determine graphs with the smallest and the largest indices.

We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tricyclic graphs, tetracyclic graphs and graphs of given order, size and number of pendant vertices. We show that all our bounds are sharp by presenting extremal graphs including graphs with symmetries. Bounds for the classical multiplicative Zagreb indices are special cases of our results.