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- URGENT!!! Using the given graph, answer the following questions: a) Write the adjacency list of the graph. b)List all the nodes of the graph in depth-first traversal starting from node 0. Note: among the possible modes to visit, from the current one, choose the node with the smallest label when you have the possibility to select from several nodes. c) List all the nodes of the graph in breadth-first traversal starting from node 0. Note: among the possible modes to visit, from the current one, choose the node with the smallest label when you have the possibility to select from several nodes.For the following graph, answer the questions. (a) Report the order of the vertices encountered on a breadth-first search starting from vertex A. Break all ties by picking the vertices in alphabetical order (i.e., A before Z). (b) Report the order of the vertices encountered on a depth-first search starting from vertex A. Break all ties by picking the vertices in alphabetical order (i.e., A before Z).[Multiple Choice D] The question(s) that follow refer to the problem of finding the minimum spanning tree for the weighted graph shown in the photo below. 9. In the given figure, using DFS traversal identify the sequence of vertices visited according to weight. a. ABCDEFG b. ABCGDEF c. AGBEFDC d. AGEBFDC e. None of the above 10. In the given figure, using BFS traversal identify the sequence of vertices visited. a. ABCDEFG b. ABCGDEF c. AGBEFDC d. AGEBFDC e. None of the above
- Create a 10 weighted connected graph with the following characteristics: • 10 vertices are alphabetically labeled starting with A. • Vertex A is not adjacent to vertex G. • At least two vertices have a degree greater than 2. • All weights are greater than 0. • No weights are the same. 1. Identify the degree of each vertex in your graph. 2. Explain whether the graph has an Euler path, using definitions, properties, or theorems. 3. Describe a path from vertex A to G. 4. Find the total weight of the path from part F3. Show all work.12- A Graph consists of four vertices A, B, C and D. If we start from A, which vertex will be visited first of all by breadth-first search (BFS) algorithm? A C D B2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
- Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: look at the picture sent Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. Which statement of the following is correct? group of answer choices a) The sequence of vertices visited using a DFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. b) The sequence of vertices visited using a BFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. c) Both sequences are wrong. d) Both sequences are correct.Let G be a graph with 7 vertices, where eachvertex is labelled by a number from 1 to 7. Twovertices are selected at random. Let us call themu and v. Now, directed edges are drawn from u toall other vertices except v and directed edges aredrawn from all vertices to v except from u. Let xbe the total possible topological sortings of G.hint: You may remember the terms factorials orfibonacci?Write down the value of x:For each graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color
- Answer the following statements as true or false regarding Prim's algorithm: a. True or False: Prim's algorithm can only be used on weighted graphs. b. True or False: Prim's algorithm will produce a graph with equal number of vertices and edgesMark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.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.