Exam 6: The Mathematics of Touring: Traveling Salesman Problems

For the weighted graph shown below, find the optimal tour and write your answer using A as the starting and ending vertex.

How many edges are there in the complete graph K12 ?

Consider the graph shown below; how many Hamilton Paths are there from vertex A to vertex F ?

-Consider the graph above ; how many Hamilton Paths are there starting at vertex A and ending at vertex F?

Suppose that in solving a TSP (traveling salesman problem) you use the cheapest-link algorithm and find that the length of the tour is 15,000 miles. If the optimal tour has a length of 12,000 miles, then what is the relative error of your cheapest-link tour? Express your answer as a percentage.

The game Doodle-Chip consists of moving a marker around a board. Once on a square, the marker can move to any other square which is adjacent (shares a side) with the square occupied. Is it possible to Place the marker on the board at position A, move to every other square once and only once, and end On square labeled B?

For the graph shown below, how many distinct Hamilton Paths start at A and end at F?

For the weighted graph shown below, apply the cheapest-link algorithm and find the cost of the resulting tour.

For the weighted graph below, apply the repetitive nearest-neighbor algorithm and give its cost.

Consider the graph shown below; how many Hamilton Paths are there from vertex A to vertex F ?

The chart below shows the one-way charge for a taxi-ride between five different cities. Give the cost of the tour found by applying the cheapest-link algorithm.

How many distinct Hamilton Circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct or different from the circuit.)

For the graph shown below, find a Hamilton Circuit using vertex A as your starting and ending point.

Draw a graph which has a Hamilton Circuit but does not have an Euler Circuit.

Consider the weighted graph given below; apply the nearest-neighbor algorithm with vertex F as a starting vertex and give the resulting tour.

For the weighted graph below, apply the repetitive nearest-neighbor algorithm and write the resulting tour using vertex D as a starting and ending vertex.

Which of the graphs below has a Hamilton Circuit?

The game Doodle-Chip consists of moving a marker around a board. Once on a square, the marker can move to any other square which is diagonal (kitty-corner) with the square occupied. Is it possible to place the marker on the board at position A, move to every other square once and only once, and end on the square labeled B? (a) Yes (b) No

For the weighted graph shown below, apply the nearest-neighbor algorithm with C as a starting vertex and find the cost of the resulting tour.

The chart below shows the average travel time in minutes between five different cities. Give the total time (cost) of the tour found by applying the cheapest-link algorithm.