  Given a graph $G$, viewed as a loop-less symmetric digraph, we study the
maximum number of fixed points in a conjunctive boolean network with $G$ as
interaction graph. We prove that if $G$ has no induced $C_4$, then this
quantity equals both the number of maximal independent sets in $G$ and the
maximum number of maximal independent sets among all the graphs obtained from
$G$ by contracting some edges. We also prove that, in the general case, it is
coNP-hard to decide if one of these equalities holds, even if $G$ has a unique
induced $C_4$.
