### Problem on Graph Theory and the Travelling Salesman Problem#### Problem Statement:This exercise revolves around the roads between towns and the length of each road in kilometers. A delivery driver resides in town D and needs to visit every other town before returning to D.#### Graph Description:- The graph has five vertices (A, B, C, D, and E) representing towns.- The edges between the vertices represent roads, and the numbers on the edges indicate the distance between towns in kilometers.#### Questions:a) Complete the graph with edges showing the least distance between each pair of towns.b) Use the nearest neighbor algorithm starting at D to find an upper bound for the Travelling Salesman Problem (TSP).c) The delivery van can travel 600 km on one tank of fuel. By applying the deleted vertex algorithm with vertex A deleted, show that the driver must refuel during the trip.#### Graph Analysis:- **Vertices (Towns):** A, B, C, D, E- **Edges (Roads with distances):** - A-B: 150 km - B-C: 250 km - C-E: 100 km - E-A: 200 km - B-D: 110 km - D-C: 80 km#### Detailed Explanation of the Graph:The graph illustrates a network where the least distances between towns have already been provided. Here are the connections with distances:1. A is connected to B with a road of 150 km2. B is connected to D with a road of 110 km3. B is connected to C with a road of 250 km4. D is connected to C with a road of 80 km5. C is connected to E with a road of 100 km6. E is connected to A with a road of 200 km#### Task Breakdown:1. **Part A: Completing the Graph:** Ensure every pair of towns (vertices) has an edge denoting the least distance between them. According to the provided graph, this step is already done.2. **Part B: Upper Bound for TSP Using Nearest Neighbour Algorithm:** Apply the nearest neighbor algorithm starting at town D: - Start at D, move to the nearest neighbor (which is C, 80 km) - From C, move to the nearest unvisited town

we are given a graph that shows the roads between towns, and the length of each road in kilometres…

This graph shows the roads between towns, and the length of each road in kilometres. В 150 A delivery driver lives in town D, and must visit every other town before returning to D. 110 a Complete the graph with edges showing the least distance between each pair of towns. 25 200 b Use the nearest neighbour algorithm starting at D to find an upper bound for the TSP. C The delivery van can travel 600 km on one tank of fuel. By applying the deleted vertex algorithm with vertex A 80 E 100 deleted show that the driver must refuel during the trip

This graph shows the roads between towns, and the length of each road in kilometres. В 150 A delivery driver lives in town D, and must visit every other town before returning to D. 110 a Complete the graph with edges showing the least distance between each pair of towns. 25 200 b Use the nearest neighbour algorithm starting at D to find an upper bound for the TSP. C The delivery van can travel 600 km on one tank of fuel. By applying the deleted vertex algorithm with vertex A 80 E 100 deleted show that the driver must refuel during the trip

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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