Transcript SECTION 5.1: Euler Circuit Problems

SECTION 5.1:
Euler Circuit Problems
What is a routing problem?
• Routing problems deal with finding ways to
deliver goods and/or services to many different
destinations. Does a possible route exist or
which one of the possible routes is the most
efficient?
• Examples of routing problems: delivering mail,
walking through a neighborhood…
• The Seven Bridges of Konigsberg: A prize is offered to
the first person who can find a way to walk across each
one of the seven bridges of Konigsberg without recrossing any and return to the original starting point.
bridge
SECTION 5.2: GRAPHS
• A graph is a picture consisting of vertices
(dots) and edges (lines). The edges do
not have to be straight lines but they have
to connect two vertices.
• Example:
or
• A loop is an edge connecting a vertex
back with itself.
This is a loop
named BB
No loop
• An isolated vertex is the vertex that is not
connected to any other vertex.
Vertex F is
an isolated
vertex
• Multiple edges have two vertices for
which there exists more than one edge
connecting them.
These are
multiple
edges CD
or DC
• Disconnected graph: a graph made up of
connected pieces
• Example:
G
• Components - pieces of disconnected
graphs which are themselves connected
• List vertex set and edge set
• Vertex set V =
• Edge set E =
Example
• Consider the graph with V={A, B, C, D, E}
and E={AC, AE, BD, BE, CA, CD, CE, DE}
Draw several different pictures of the graph.