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Maths Week 11 Graded Assignments IIT Madras

Maths week 11 graded assignment Complete  Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments 

1. An undirected graph G has 26 vertices and the degree of each vertex is at least 6. What is the minimum number of edges that the graph G can have?
 
1 point

 

 
 
2. If G is a connected undirected graph such that every vertex has degree at most 9 , and the shortest path between any two vertices has length at most 2, then what is the maximum number of vertices in G? (Hint: Try to draw the BFS tree starting with any vertex)
 
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3. Suppose  is the adjacency matrix of a connected undirected graph . If �2=[111011111101111110011111101111110111] and the shortest path between any two vertices has length at most 2, then which of the following may represent the graph ?
 
 
1 point
 
4. Suppose  is a graph with 6 vertices {0,1,2,3,4,5} and the adjacency matrix of the graph  is �=[001001000001000100000000110000000000]. Which of the following statements is True?
 
 
 
 
 
 
 



USE THE FOLLOWING INFORMATION FOR QUESTIONS [7-8]:
Shreya needs to perform 10 tasks namely {�,�,�,�,…..�}. Some tasks needs to be performed after performing a particular task. In the below table, column 1 shows the tasks and column 2 shows the sets of tasks that can be performed only after performing the particular task.

                                                                                       

 
 
1 point
Which of the following sequences may represent the possible order in which Shreya can perform the tasks?
 
 
 
 
 
 
 
 
 
If each task takes 5 minutes to complete and she performs all the independent tasks simultaneously, then the time(in minutes) taken by Shreya to complete all the tasks is
 
1 point



 
 
1 point
 
An undirected weighted graph  is shown below. Find the set of all positive integer values of  such that if we use Dijkstra’s algorithm, there will be a unique shortest path from vertex  to vertex  that contains the edge (�,�).


 
 
 
 
 
 
 
 
 
 
1 point
 
A directed graph  is shown below. Suppose we are trying to perform an algorithm to find the shortest path from vertex �0 to �4. Which of the following statements is (are) correct?


 
 
 
 
 
 
 
 
 
 
1 point
Which of the following statements is (are) INCORRECT?
 
 
 
 
 
 
 
 


(Use the following information for questions 10 & 11)

 
 
 
An employee of that company wanted to travel from the city �2 to the city �5. If he travelled by the cheapest route possible, then the total fare (in thousands of rupees) he paid for flight journey was
 
 
1 point
 
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If an inspection team member wanted to inspect all the branches of the company starting from �2 and ending at �5, visiting each branch exactly once, then which of the following routes should he choose in order to pay minimum fare for flight journey?
 
 
 
 
 
 
 


(Use the following information for questions 12 & 13)

 
 
What is the total maintenance cost (in hundreds of rupees) of the optimum subset of links?
 
1 point
 
Find the number of different ways of choosing an optimum subset of links for the given graph.
 
1 point


(Use the following information for questions 14 & 15)



 
 
1 point
 
Suppose we perform Prim’s algorithm on the graph  starting from vertex  to find an MCST. Then the order in which the vertices are added is
 
 
 
 
 
 
 
 
 
 
1 point
 
Suppose we perform Kruskal’s algorithm on the graph  starting from vertex  to find an MCST. Which of the following edges are not added to the minimum cost spanning tree?
 
 
 
 
 
 
 
 

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