Exam 7: Graph Theory

Suppose you tell a story to two of your friends. Some people repeat the story to two others, and in turn some of these 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, it turns out that 384 people have heard the story, but not related it to others. How many people have heard the story from others?

If a graph has a vertex of degree _____, then each edge meeting that vertex must be part of any Hamilton circuit.

In a tree, if a parent has the level of 2, then what is the level of the grandchildren?

In a complete binary tree of height H, the number of parents equals _________.

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

Suppose that a graph containing four vertices A, B, C, and D has an Euler circuit starting from A. If the degree of the vertex B is 4, then how many times will the Euler circuit pass the vertex B?

A circuit or cycle in a graph is a path that begins and ends at the same vertex.

There are 65 members of an organization. The plan for disseminating news requires one member to contact two others with the information. Each member who receives the news contacts two members who have not yet gotten the news. This continues until all members have the information. How many members contact others?

What is the level of the root of a tree?

Find an Euler circuit for the figure below.