Network Definitions
Eulerian and Hamiltonian
Planar Graphs
Adjacency Matrices
100
Define a walk
Any route through a network
100
Define an Eulerian Graph
A trail that traverses every edge once and starts and finishes at the same vertex.
100
Define a planar graph
When a graph can be redrawn with no intersecting edges
100
How many vertices are in this network?
4
200
Define a Trail
A walk that does not repeat any edges
200
Define a Hamiltonian Path (Cycle)
A path that visits each vertex once and starts and finishes at the same vertex. (Can repeat the start and finishing vertex)
200
How many faces does this graph have?
6
200
What does the highlighted rectangle tell you about about the network?
The network is disconnected
300
Define a Path
A walk that does not repeat any vertices
300
How can you use the degrees of the vertices of a network to show a graph has a Semi-Eulerian trail.
If the graph has a pair of odd degree vertices then there must be a Semi-Eulerian trail.
300
Recall Euler's formula
v+f-e=2
300
What does the circled number 1 tell you about the network?
The network has a loop
400
Define a cycle
A path that starts and finishes at the same vertex.
OR
A walk that does not repeat vertices that starts and finishes at the same vertex.
400
How can you use the degrees of the vertices of a network to show a graph is Eulerian?
If the degrees of the vertices are all even then the graph is Eulerian which means an Eulerian trail is possible.
400
Is the following graph planar?
Yes
400
What does a leading diagonal of zeroes tell you about the network?
There are no loops at any vertex.
500
Define a Closed Trail
A trail that starts and finishes at the same vertex.
OR
A walk that does not repeat edges and starts and finishes at the same vertex.
500
Classify the graph below 
Semi-Hamiltonian
500
How many faces will there be if a planar graph has 7 edges and 5 vertices
4
500
What is the degree at the first vertex
1