Use the Edge-Picking Algorithm to find a Hamiltonian circuit in the weighted graph.FEA-F-D-E-B-C-AA-D-B-F-E-C-AA-B-E-D-F-C-AO A-C-D-E-F-B-AO A-E-B-C-F-D-AD2B3с

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Answered: Use the Edge-Picking Algorithm to find…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Hamiltonian Circuits and The Traveling Salesman Problem Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost? A B C D E F What is the lowest cost circuit produced by the repeated nearest neighbor algorithm? Give your answer as a list of vertices, starting and ending at the same vertex. Example: ABCDEFA
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Consider the directed acyclic graph (DAG) D shown below. (a) Write down the adjacency matrix A corresponding to the ordering of the verticesgiven by alphabetical order : a, b, c, d, e, f, g.(b) Find all permutations of the set of vertices {a, b, c, d, e, f, g} such that the associated adjacency matrix is strictly lower triangular.(c) Find the number of spanning trees rooted at vertex g
a) List all the odd vertices of the graph.b) According to Euler’s Theorem, does the graph have an Eulerian circuit? Howdo you know?c) According to Euler’s Theorem, does the graph have an Eulerian path? Howdo you know? What is the difference between a Hamiltonian path and an Eulerian path? A person starting in Columbus must-visit Great Falls, Odessa, andBrownsville (although not necessarily in that order), and then return home toColumbus in one car trip. The road mileage between the cities is shown Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex. Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in…
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Use the Repeated Nearest Neighbor Algorithm to find an approximation for the optimal Hamiltonian circuit. 1. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex A is . The sum of it's edges is . 2. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex B is . The sum of it's edges is . 3. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex C is . The sum of its edges is . 4. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex D is . The sum of it's edges is . 5. The Hamiltonian circuit giving the approximate optimal solution using the Repeated Nearest Neighbor Algorithm is . The approximate optimal solution is . IMAGE BELOW

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Use the Edge-Picking Algorithm to find a Hamiltonian circuit in the weighted graph. F E A-F-D-E-B-C-A A-D-B-F-E-C-A A-B-E-D-F-C-A O A-C-D-E-F-B-A O A-E-B-C-F-D-A D 2 B 3 с