Question 1
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1 II. 6, 6, 6, 6, 3, 3, 2, 2 III. 7, 6, 6, 4, 4, 3, 2, 2 IV. 8, 7, 7, 6, 4, 2, 1, 1
Question 2
The time complexity of computing the transitive closure of a binary relation on a set of n elements is known to be:
Question 3
The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity.
Question 4
Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct?
Question 5
Question 6
Which of the following statements is/are TRUE for an undirected graph?
P: The number of odd-degree vertices is even
Q: Sum of degrees of all vertices is even
Question 7
Question 9
Question 10
There are 38 questions to complete.