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

See similar textbooks

Similar questions

solute question 4，please
Provide an easy-to-understand explanation for the direct proof problem below: For every graph that is undirected (no self-loops or multi-edges) with n nodes, if every node has degree > n/2 then there exists a cycle of length 3.
Chads baseball team is practicing hitting in the batting cages for pitching machines pitch baseballs at the rate of 35 pitches in 5 minutes chad practiced hitting for 8 minutes how many baseballs were pitched to chad in that time
In Cay({(1, 0), (0, 1)}:Z4 ⊕ Z5), find a sequence of generators thatvisits exactly two vertices twice and all others exactly once and returnsto the starting vertex.
9. For the question use Fluery's Algorithm. Go to the slide 18 -21 in the PowerPoint of the Sec 14.2 and follow similar steps with at least 4 figures to find your Euler Circuit. Start the Euler Circuit at B. E C. A
7. Use Dijkstra's Algorithm to find the lowest weighted path between vertices a and f for the graph D pictured below. (This is NOT the same weighted graph as in Question 6.) 4 IN 7 8. Find x(I) for the graph I pictured below. A
In Cay({(1, 0), (0, 1)}:Z4 ⊕ Z5), find a sequence of generators thatvisits exactly one vertex twice and all others exactly once and returnsto the starting vertex.
Examine the graph to the right. a. Determine whether the graph has an Euler path, an Euler circuit, or neither. b. If the graph has an Euler path or circuit, use trial and error or Fleury's algorithm to find one. The graph has an Euler circuit. The graph has an Euler path (but not an Euler circuit). The graph has neither an Euler path nor an Euler circuit CADB Drag the correct answers into the boxes below. If an Euler path or an Euler circuit exists, drag the vertex labels to the appropriate locations in the path. If no path or circuit exists leave the boxes in part (b) blank a. Does the graph have an Euler path, an Euler circuit, or neither? b. If the graph has an Euler path or an Euler circult, use trial and error or Fleury's algorithm to find one starting at A
Examine the graph to the right. a. Determine whether the graph has an Euler path, an Euler circuit, or neither. b. If the graph has an Euler path or circuit, use trial and error or Fleury's algorithm to find one. A The graph has an Euler circuit. The graph has an Euler path (but not an Euler circuit). The graph has neither an Euler path nor an Euler circuit. BAC D Drag the correct answers into the boxes below. If an Euler path or an Euler circuit exists, drag the vertex labels to the appropriate locations in the path. If no path or circuit exists, leave the boxes in part (b) blank. a. Does the graph have an Euler path, an Euler circuit, or neither? b. If the graph has an Euler path or an Euler circuit, use trial and error or Fleury's algorithm to find one starting at B. B, ,A, D, ....
Consider the following graph. Show the coloring produced by the greedy algorithm when the vertices are colored in the following order.
3. To defeat Electro, Spider-Man needs to connect all the pylons (vertices) in the graph below with his webbing to form an electric circuit, with the numbers representing the difficulty of making the connection. Show that the Nearest Neighbor algorithm will NOT work for Spidey for this given graph. Try at least two different starting points, one of which should be the top left corner. 3 11 3 12 5 2 9 14 1 8 7 10 9 0 13 16