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- Note: Solve the following question and please don't repost previous answers and don't give a computer generated answer. Problem: Draw a simple, connected, directed, weighted graph with 9 vertices and 17 edges, each with unique edge weights. Identify one vertex as a “start” vertex and illustrate a running of Dijkstra’s algorithm on this graph.Consider the undirected graph in Figure 1.a) Write down the adjacency matrix and adjacency lists specifying this graph. Assume that therows, columns and vertices in the adjacency list follow the alphabetical order of the vertex labels.b) Starting at vertex "S' and resolving ties by the vertex alphabetical order, traverse the graphby breadth first search and construct the corresponding breadth first search tree.Q1) how many graphs are there on 20 nodes? (To make this question precise, we have to make sure we known what it mean that two graphs are the same . For the purpose of this exercise,we consider the nodes given and labeled,say,asAlice ,Bob,...... The graph consisting of a single edge connecting Alice and Bob is different from the graph consisting of a single edge connecting Eve and frank.) Q2) Formulate the following assertion as a theorem about graphs and prove it :At every party one can find two people who know the same number of other people (like Bob and Eve in our first example).
- A manufacturer of chemical goods is faced with the problem that certain goods cannot be stored at the same place due to the danger of unwanted reactions. What he seeks is a storage scheme such that goods that cannot be located at the same place are indeed separated. Provide a graph model to solve this problem. Do not write details of any algorithms. Simply describe your graph vertices, edges, and the classic graph theory problem that is useful for the design of the storage scheme here.1.Write the Vertex set V of the graph. 2.Write the Edge set E of the graph 3.Analyze the Edge graph and explain if the Transitive relation r exists for graph G. 4.If the transitive relation don’t exist apply Warshall Algorithm (step by step) to satisfy transitive relation for G by Transitive closure. 5.Redraw the graph with transitive closure as per the final matrix made using Warshall AlgorithmThis is an MCQ give proper explanation don't copy from google Graph Algorithm Think of a undirected graph in which node A is connected to four other nodes, say, B, C, D and E, via an edge of weight 2. Which of the following statements is definitely false? 1) The shortest path from node C to node D is 30. 2) The shortest path from node C to node D is 2. 3) The shortest path from node C to node D is 4.
- The following table presents the implementation of Dijkstra's algorithm on the evaluated graph G with 8 vertices. a) What do the marks (0, {a}) and (∞, {x}) in the 1st row of the table mean? b) What do the marks marked in blue in the table mean? c) Reconstruct all edges of the graph G resulting from the first 5 rows of the table of Dijkstra's algorithm. d) How many different shortest paths exist in the graph G between the vertices a and g?PROBLEM 2. 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: 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.a. Draw G.b. Give the sequence of vertices of G visited using a DFS traversal starting at vertex 1.c. Give the sequence of vertices visited using a BFS traversal starting at vertex 1.a) Illustrate the sequence of vertices of this graph visited using depth-first search traversal starting at vertex g. b) Illustrate adjacency list representation and adjacency matrix representation, respectively, for this graph. What are the advantages and disadvantages of those two representations? c) Describe an algorithm to find in the graph a path illustrated below that goes through every edge exactly once in each direction.
- please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?Suppose we want to use UCS and the A* algorithm on the graph below to find the shortest path from node S to node G. Each node is labeled by a capital letter and the value of a heuristic function. Each edge is labeled by the cost to traverse that edge. Perform A*, UCS, and BFS on this graph. Indicate the f, g, and h values of each node for the A*. e.g., S = 0 + 6 = 6 (i.e. S = g(S) + h(S) = f(S)). Additionally, show how the priority queue changes with time. Show the order in which the nodes are visited for BFS and UCS. Show the path found by the A*, UCS, and BFS algorithms on the graph above. Make this example inadmissible by changing the heuristic value at one of the nodes. What node do you choose and what heuristic value do you assign? What would be the A* algorithm solution then.