slide task 6

FIREWIRE

TASK 6-Graph teory-

WHAT DO YOU UNDERSTAND ABOUT :

Euler Path Euler Circuit

DEFINITION EULER PATH

is a path that uses every edge of a graph exactly once.

EULER PATH EXAMPLE

DEFINITION EULER CIRCUIT

is a circuit that uses every edge of a graph

exactly once.

EULER CIRCUIT EXAMPLE

DIFFERENCES BETWEEN EULER PATH AND EULER CIRCUIT

Euler Path-starts and ends at different

vertices. Euler circuit- when a Euler path

begins and ends at the same vertex

STEP BY STEP TO DETERMINE EULER PATH AND EULER CIRCUIT

There are two odd vertices, A and F. Let's start at F.

Start walking at F. When you use an edge, delete it.

Path so far: FEACB

Path so far: FEACBD.

Path so far: FEACBDC

Path so far: FEACBDC Now we have to cross the bridge CF.

WHAT DO YOU UNDERSTAND ABOUT:

Hamilton PathHamilton Circuit

DEFINITION AND EXAMPLE OF HAMILTON PATH

Definition: a directed path that goes through each vertex exactly once

DEFINITION AND EXAMPLE OF HAMILTON CIRCUIT

 is a circuit (a path that ends where it starts) that visits each vertex once without touching any vertex more than once. There may be more than one Hamilton path for a graph

DIFFERENCES BETWEEN HAMILTON PATH AND HAMILTON CIRCUIT

Hamilton PathA path must have beginning and ending.

Hamilton CircuitDoes not have beginning / start & end is

same.

STEP BY STEP TO DETERMINE HAMILTON PATH AND CIRCUIT

a b

cd

a

b

cd

e