Fixed points and maximal independent sets in AND-OR networks

We study the maximum number of fixed points of boolean networks with local update function AND-OR. We prove that this number for networks with connected digraph is 2^(n-1)/2 for n odd and 2^(n-2)/2+1 for n even if the digraph has not loops; and 2^n-1+1 otherwise, where n is the number of nodes of the digraph. We also exhibit some networks reaching these bounds. To obtain these results we construct a bijection between the maximal independent sets of the digraph and the fixed points of the network belonging to a particular family of AND-OR networks.