A B A B C 3 20 15 CDE 1 3 20 57 33 F 38 5378 15 13 27 -- 56 D 57 13 56 -- E F 33 38 27 58 6 37 52 44 47 6 52 37 44 47 == The weights of edges in a graph are shown in the table above. Apply the nearest neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
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- The Brute-Force Bandits is a rock band planning a five-city concert tour. The cities and the distances (in miles) between them are given in the weighted graph below. The tour must start and end at A. The cost of the chartered bus in which the band is traveling is $8 per mile. a)The nearest-neighbor tour with starting vertex A is? and the cost of the tour? b) The nearest-neighbor tour with Starting vertex B is? and the cost of the tour?Discrete Maths Oscar Levin 3rd eddition 4.1.15: Prove that any graph with at least two vertices must have two vertices of the same degree. ps: I'd be so glad if you include every detail of the solution.an "x" in the table below indicates a direct route between the corresponding cities. draw a graph that represents this information, in which each vertex represents a city and an edge connects two vertices if there is a train route between the corresponding cities. city A B C D E F A - X X B - X X X C X - X X X D X X - E X X X - X F X X X -
- Consider the following graph. (Enter your answers as comma-separated lists.) A graph with 5 vertices and 7 edges is shown. Loop e1 connects vertex v1 and vertex v1. Edge e2 connects vertex v1 and vertex v2. Edge e7 connects vertex v1 and vertex v3. Loop e3 connects vertex v2 and vertex v2. Edge e6 connects vertex v2 and vertex v3. Edge e4 connects vertex v2 and vertex v5. Edge e5 connects vertex v2 and vertex v5. Vertex v4 is isolated. (a) Find all edges that are incident on v1. (b) Find all vertices that are adjacent to v3. (c) Find all edges that are adjacent to e1. (d) Find all loops. (e) Find all parallel edges. (f) Find all isolated vertices. (g) Find the degree of v3.a. Define the following with an example; i. pathsii. simple graphb.Draw the graph with the adjacency matrixordering of vertices, a, b, c, d.030253 0 1 17 with respect to the 01122120i. Find the degree of each vertex in your graph from part (a) above.ii. How many walks of length 2 are there from the vertex c to c? How manyof these walks are paths?4. a. Define the following Terms giving one example each: i. Partial Ordering Relationsii. Equivalence relationsb. Answer these questions for the partial order represented by the following Hasse