GATE 2023 CS – Question 56

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 $A \subset B$ or $B \subset A$. 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 (BFS) starting from A is denoted by $B(A)$. If $\emptyset$ denotes the empty set, then the cardinality of $B(\emptyset)$ is ______.