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- Given the unconnected graph shown below, where the edges that are possible are shown as dashed lines with their associated costs, which of the following answers represents the minimum spanning tree for the graph? The original graph is the one with dotted lines that are NOT red.a) Explain how graphs can be used to model electronicmail messages in a network. Should the edges be directedor undirected? Should multiple edges be allowed?Should loops be allowed?b) Describe a graph that models the electronic mail sentin a network in a particular week.Question 1. Describe differences between breadth-first and depth-first searches and provide a sequence for each of the searches for the following graph: A / \ B C / / \ D E F Question 2. For the graphs shown below, provide at least 2 BFS and 2 DFS Traversal Paths for each. See starting nodes in bold below for each graph. Left Graph BFS 1: 1 BFS 2: 4 DFS 1: 1 DFS 2: 4 Right Graph BFS 1: 1 BFS 2: 10 DFS 1: 1 DFS 2: 10
- Your colleague needs to implement a search algorithm to apply to a particular problem they are facing. The problem has the following characteristics: ● The graph representing the problem has a very high forward branching factor. ● The graph is dynamically generated (i.e. it is not a static graph). ● There will be some cycles in the graph . ● There is reason to believe that the goal state will be very deep in the graph. ● There is an efficient method of estimating how far each state is from the goal, and an estimate will always be less than or equal to the actual cost . Of the search algorithms we have covered, which would you recommend to your colleague, and why? Be very detailed in justifying this choice and providing advice about things they should pay special attention to.Which of the following best states the property of a spanning tree of a graph M? 1. It is always acyclic.2. It does not include each vertex of the graph M. 3. It is not a subgraph of M. 4. The graph M has only one spanning tree.a) Write the adjacency matrix representing the graph above. b)Would you prefer to represent this graph (specifically the one above) as an adjacency list or as an adjacency matrix? Justify your answer. c) Topological sorting is an algorithm on graphs used to produce a schedule. Assuming each node in this graph represents an item, what is ONE schedule associated with the above graph? If the topological sorting algorithm cannot be run on the above graph, justify your answer.
- 9) Given the following graph and the source node F (the 1st node to be discovered), which of the following could be the 3rd node to be discovered during a DFS? A. A B. E C. B D. J E. Allfunction [ ] = square_spectrum( L,N )%Activity 1 for CEN415 Summer 2022 x=linspace(0,2*L,200);f1=(-1).^floor(x/L);plot(x,f1)f2=0;for n=1:2:N, f2=f2+4*sin(n*pi.*x/L)/n/pi;endhold onplot(x,f2)hold offend Q1= Which one is true? a. When the N increases, the approximated graph tends to be closer to the original square wave b. When the L increases, the approximated graph tends to be closer to the original square wave c. When the L decreases, the approximated graph tends to be closer to the original square wave d. When the N decreases, the approximated graph tends to be closer to the original square wave e. NoneA weighted, directed graph is a suitable representation to represent the daily airline routes flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg. Draw a graph that represents this problem
- Pick the correct statements for the attached directed graph for a toy world wide web. 1. There are exactly six columns having a 1 as an entry. 2. If a new edge from node I to F is added, the resulting graph is strongly connected. 3. The smallest non-zero element in the link matrix is 1/4. 4. The link matrix Q has a column of all zeros. 5. The link matrix is a reducible matrix.3.Consider this graph data:- Jessica's buddy list: Meghan, Alan, Martin.- Meghan's buddy list: Alan, Lori.- Toni's buddy list: Lori, Meghan.- Martin's buddy list: Lori, Meghan.- Alan's buddy list: Martin, Jessica.- Lori's buddy list: Meghan.a. Compute the in/out degree of each vertex. Is the graph connected?b. Who is the most popular? Least? Who is the most antisocial?c. If we're having a party and want to distribute the message the most quickly, who should we tell first?You'd like to study social networks. Consider the following 26 people {A,B,C,...,X,Y,Z} in a social network graph. (These people can be thought of as "nodes" or points drawn on a piece of paper.) Here, we'd like to model "followers." How many different ways can we draw arrows between two people from these 26? Here, "A-->B" (A is a follower of B) is not the same as "B-->A" (B is a follower of A). Order matters here. Enter your answer as a whole number.