GATE 2023 · CS - Forenoon
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 ≠ B, and (ii) either A is a proper subset of B or B is a proper subset of 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 the empty set is denoted by {}, then the cardinality of B({}) is __________.