On the number of cliques and cycles in graphs

We give a new recursive method to compute the number of cliques and cycles of a graph‎. ‎This method is related‎, ‎respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph‎. ‎In particular‎, ‎let G be a graph and let \overline {G} be its complement‎, ‎then given the chromatic polynomial of \overline {G}‎, ‎we give a recursive method to compute the number of cliques of G‎. ‎Also given the adjacency matrix A of G we give a recursive method to compute the number of cycles by computing the sum of permanent function of the principal minors of A‎. ‎In both cases we confront to a new computable parameter which is defined as the number of disjoint cliques in G‎.