University of IsfahanTransactions on Combinatorics2251-86572220130601On the number of cliques and cycles in graphs2733287210.22108/toc.2013.2872ENMasoudAriannejadUniversity of zanjanMojganEmamiDepartment of Mathematics, University of ZanjanJournal Article20121203We 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 $G$.https://toc.ui.ac.ir/article_2872_183b76bba4970596525b994ca1ef4997.pdf