MTH 113 Exam 3

Edge

line segment connecting two vertices

What is a Hamiltonian circuit?

A Hamiltonian circuit is a circuit that uses every vertex only once except the starting one.

What is a Hamiltonian path?

A Hamiltonian path is a path that uses every vertex only once.

Vertex

A single point

What is an Euler circuit?

An Euler circuit is a circuit that uses every edge of a graph once and only once. Euler circuit starts and ends at the same vertex.

What is an Euler path?

An Euler path is a path that uses every edge of a graph once and only once and starts and ends at different vertices..

State the Euler circuit theorem.

If a graph is connected and all its vertices are even, then it has Euler circuits. If the graph has any odd vertices, then it has no Euler circuits.

What is Euler path theorem?

If a graph is connected and has exactly 2 odd vertices, then it has Euler paths. If a graph has more than 2 odd vertices, then it has no Euler paths.

State the definition of a bridge of a graph.

If the removal of one edge makes the graph disconnected, then this edge is called a bridge.

State the pros and cons of the nearest neighbor method.

Pro: forces you to try to start at every vertex, thereby giving you a better chance of find the best solution. Con: slow

State the pros and cons of the brute force method.

Pro: in theory can solve any traveling salesman problems Con: can only be used on small problems, limited practical use