MLA Exam 1
For the traveling salesman problem (Hamiltonian circuit) applied to five cities, how many distinct tours are possible?
120
For the traveling salesman problem (Hamiltonian circuit) applied to four cities, how many distinct tours are possible?
24
For the traveling salesman problem applied to seven cities, how many distinct tours are possible
5040
A graph that is not connected must have at least one vertex with valence 0
False
A spanning tree of a graph must contain every edge of the graph.
False
The circuit produced by the sorted-edges algorithm when solving the traveling salesman problem may be dependent on the starting city.
False
The nearest-neighbor algorithm for solving the traveling salesman problem always gives optimal results
False
The nearest-neighbor algorithm for solving the traveling salesman problem always produces the same result as the sorted-edges algorithm.
False
The sorted-edges algorithm for solving the traveling salesman problem always gives optimal results
False
For which of the two situations below is it desirable to find an Euler circuit or an efficient eulerization of a graph? I. A pizza delivery person takes pizzas to ten houses in a neighborhood and then returns to pick up the next set to be delivered. II. A postal carrier picks up mail from six collection boxes around a city.
Neither I nor II
For which of the two situations below is it desirable to find an Euler circuit or an efficient eulerization of a graph? I. After a storm, a health department worker inspects all the houses of a small village to check for damage. II. A veteran planning a visit to all the war memorials in Washington, D.C. plots a route to follow.
Neither I or II
Can a graph with four vertices have vertices with valences 1, 1, 2, and 3?
No
On a map there are roads from town A of length 10, 26, 12, and 50 miles. Using the nearest-neighbor algorithm for finding a Hamiltonian circuit starting at town A, which road would be traveled first?
Road of length 10
After a major natural disaster, such as a flood, hurricane, or tornado, many tasks need to be completed as efficiently as possible. For which situation below would finding an Euler circuit or an efficient eulerization of a graph be the appropriate mathematical technique to apply?
The Department of Public Works must inspect all streets in the city to remove dangerous debris
Which of the following defines the valence of vertex A of a graph?
The number of edges meeting at vertex A
When Kruskal's algorithm is used to find a minimum-cost spanning tree on a graph, which of the following is false?
The tree is not necessarily connected.
Every graph with an Euler circuit has only vertices with even valences.
True
Kruskal's algorithm for finding minimum-cost spanning trees always gives optimal results
True
The circuit produced by the nearest-neighbor algorithm when solving the traveling salesman problem may be dependent on the starting city.
True
The minimum-cost spanning tree produced by applying Kruskal's algorithm may contain the most expensive edge of the graph.
True
The minimum-cost spanning tree produced by applying Kruskal's algorithm will always contain the lowest cost edge of the graph.
True
Suppose a college campus decides to install its own phone lines connecting all of the buildings where calls may be relayed through one or more buildings before reaching their destination. The technique most likely to be useful in solving this problem is:
applying Kruskal's algorithm for finding a minimum-cost spanning tree for a graph
Suppose an architect needs to design an intercom system for a large office building. The technique most likely to be useful in solving this problem is:
applying Kruskal's algorithm for finding a minimum-cost spanning tree for a graph
Suppose the edges of a graph represent streets that must be checked by a worker from the Department of Public Works. In order to eulerize the graph, we must add three edges. The real world interpretation of this is:
we must travel three blocks twice in our circuit
