When we create a Hamiltonian circuit in a graph, it is a closed loop. We can start at any vertex, follow the path, and arrive back at the starting vertex. For instance, if we use the greedy algorithm to create a Hamiltonian circuit starting at vertex A, we are actually creating a circuit that could start at any vertex in the circuit. If we use the greedy algorithm and start from different vertices, will we always get the same result? Try it on Figure lat the left. If we start at vertex A, we get the circuit A-C-E-B-D-A, with a total weight of 26 (see Figure 2). However, if we start at vertex B, we get B-E-D-C-A-B, with a total weight of 18 (see Figure 3). Even though we found the second circuit by starting at B, we could traverse the same circuit beginning at A, namely A-B-E-D-C-A, or, equivalently, A-C-D-E-B-A. This circuit has a smaller total weight than the first one we found. D. gure 1

When we create a Hamiltonian circuit in a graph, it is a closed loop. We can start at any vertex, follow the path, and arrive back at the starting vertex. For instance, if we use the greedy algorithm to create a Hamiltonian circuit starting at vertex A, we are actually creating a circuit that could start at any vertex in the circuit. If we use the greedy algorithm and start from different vertices, will we always get the same result? Try it on Figure lat the left. If we start at vertex A, we get the circuit A-C-E-B-D-A, with a total weight of 26 (see Figure 2). However, if we start at vertex B, we get B-E-D-C-A-B, with a total weight of 18 (see Figure 3). Even though we found the second circuit by starting at B, we could traverse the same circuit beginning at A, namely A-B-E-D-C-A, or, equivalently, A-C-D-E-B-A. This circuit has a smaller total weight than the first one we found. D. gure 1

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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