A DFS of a directed graph always produces the same number of tree edges, i.e., independent of the order in which vertices are considered for DFS. State true or false.a)Falseb)True

Which of the following statements is true regarding DFS and cycles in directed graphs?2 pointsDFS can detect cycles only in undirected graphs, not in directed graphsDFS can detect cycles in directed graphs by keeping track of visited verticesDFS cannot detect cycles in directed graphs; it requires a separate algorithmDFS can only detect cycles in directed graphs if they are Hamiltonian cycles

If the DFS tree does not have any back edges, then there are no cycles in the graph. Group of answer choices True False

Which of the following options are true regarding DFS and BFS traversals in the given graph starting with vertex 1? Both DFS and BFS will always visit the vertices in the same order. DFS order of traversal need not be the same as the BFS order of traversal for the give graph.

An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components. Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following options is/are correct?Note: This kind of question will be helpful in clearing CTS recruitment.

Any graph is a tree if and only if the graph is.... Question 32Select one: A directed graph Completely connected Contains no cycles