Exam 7: Graph Theory

What is the degree of vertex F?

If a circuit traverses each edge of the graph exactly once, it is called a(n) _____________ circuit.

What size dictionary can be accommodated by a spell-checker that uses 30 checks?

A traveling salesman must visit all four cities indicated in the figure below. Which is the shortest route he can take if he wants to begin and end in city A?

Suppose you tell a story to two of your friends. Some people repeat the story to two others, and in turn some pass the story on. Each time the story is told, it is told to two new people and no one hears the story twice. Sometime later, 271 people know the story. How many people have related the story to others?

One night you put a quarter into a slot machine and get back two quarters. The next night, you put these two quarters back in the machine one at a time, and each time two quarters came out. This pattern continued through the sixth night, after which you took your winnings and went home. How many quarters were fed into the machine?

What is the degree of each vertex in the figure below?

You want to use a dictionary so that you have to check any word at most six times. How big a dictionary can you accommodate?

Every vertex of a tree is either a parent or a _______________ but not both.

Find an Euler circuit for the figure below.

When graphs are represented pictorially using dots and segments, the dots are called ___________.

On a complete graph with n vertices, there are n!/2 Hamilton circuits starting at a given vertex, not counting reverse routes. If a traveling salesman wanted to make deliveries to nine cities in a region, how many possible routes would he have to check to find the shortest one?

The following table shows the distance (in miles) between cities A, B, C, and D. When a traveling salesman visits all four cities, how many miles does he travel if he uses the cheapest link algorithm?

We have a dictionary consisting of 500 words. If we use a binary tree as a spell-checker, how many checks might be required to test whether "tat" is a valid word?

A binary tree is _______________ if all the leaves are at the highest level.

The largest level of the tree is called the _____________.

One night you put a quarter into a slot machine and get back two quarters. The next night, you put these two quarters back in the machine one at a time, and each time two quarters came out. This pattern continued through the sixth night, after which you took your winnings and went home. How much money did you take home?

Finding a Hamilton circuit with the shortest distance for a given complete graph is called _______________.

If a complete graph has five vertices, then how many edges are in the graph?

A spell-checker is using a binary tree. If the size of the dictionary doubles, what will be the increase in the number of required checks?