GATE | CSE 2023 | Question 56

Let U = {1, 2, 3}. Let 2U denote the powerset of U . Consider an undirected graph G whose vertex set is 2U. For any A, B ∈ 2U, (A, B) is an edge in G if and only if (i) A /= B,  and (ii) either A Ç B or B Ç 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 ∅ denotes the empty set, then the cardinality of B(∅) is _______________

(A)

(B)

(C)

(D)