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) $$A \ne B$$, and (ii) either $$A \supseteq B$$ or $$B \supseteq A$$. 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 $$\phi$$ denotes the empty set, then the cardinality of B($$\phi$$) is ___________
Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of
Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?
The following simple undirected graph is referred to as the Peterson graph.
Which of the following statements is/are TRUE?
The following graph is isomorphic to the Peterson graph.
