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 andto the sum of permanent function over all principal minors of the adjacency matrix of the graph. inparticular, let g be a graph and let g be its complement, then given the chromatic polynomial of g,we give a recursive method to compute the number of cliques of g. also given the adjacency matrix aof g we give a recursive method to compute the number of cycles by computing the sum of permanentfunction of the principal minors of a. in both cases we confront to a new computable parameter whichis dened as the number of disjoint cliques in g.