Q46

Let $U=\{1,2,3\}$. Let $2^{U}$ denote the powerset of $U$. Consider an undirected graph $G$ whose vertex set is $2^{U}$. For any $A, B \in 2^{U},(A, B)$ is an edge in $G$ if and only if (i) $A \neq B$, and (ii) either $A \subsetneq B$ or $B \subsetneq A$. For any vertex $A$ in $G$, the set of all possible orderings in which the vertices of $G$ can be visited in a Breadth First Search $\text{(BFS)}$ starting from $A$ is denoted by $\mathcal{B}(A)$. If $\emptyset$ denotes the empty set, then the cardinality of $\mathcal{B}(\emptyset)$ is ______________.