Networks Definitions 3A recap

​NETWORKS DEFINTIONS

By Narelle Pritchard

Vertex Edge Faces

Vertex - an object/place represented by a dot

Edge - a connection between two vertices represented by a line

Faces - inclosed areas +1 for the outside

Fill in the Blanks

How many vertices are there?

Fill in the Blanks

How many edges are there?

Fill in the Blanks

How many faces are there?

Loop

an edge, that connects a vertx back to its self, without going through any other vertex.

Drag and Drop

This is network has one ​

Placeholder

Drag these tiles and drop them in the correct blank above

loop

vertex

face

edge

Fill in the Blanks

How many vertices have multiple edges?

Simple Graph

a graph that does not contain a loop or multiple edges

Multiple Choice

Are these all simple graphs?

• YES

• NO

Degree of a vertex

The degree of a vertex is the number of edges connected to a vertex.
A loop counts as two edges for the degree.

Multiple Choice

Which statement is true

• deg (A) = 5

• deg (B) = 5

• deg (C)= 5

Drag and Drop

A vertex that has a degree of zero, is said to be ​

Placeholder

Drag these tiles and drop them in the correct blank above

isolated

simple

connected

isomorphic

Degenerate Graph

​a graph where all vertices are isolated

Multiple Choice

Is this an example of a Degenerate Graph?

• YES

• NO

​Question:
Consider the network diagram below.
The vertices are labelled A, B, C, D, E, F, G.

Edges are drawn as shown:
A is connected to B, C, D.
B is connected to A, C.
C is connected to A, B, D, E.
D is connected to A, C and has a loop
E is connected to C, F. F is connected to E. G has no edges.

Multiple Choice

Identify the isolated vertex

• D

• E

• F

• G

Fill in the Blanks

How many edges are in the network?

Fill in the Blanks

How many faces are in the network?

Sum of degrees

sum of the degrees = 2 x number of edges

adding up all of the degrees in a network

​For example:

22 degrees
and ... 11 edges

Odd and even degree

​VERTEX

Odd: a vertex that has an odd number for the degree

Evan: a vertex that has an even number for the degree

Multiple Choice

How many vertices have an odd degree?

• 1

• 2

• 3

• 4

Multiple Choice

Is it possible to have a network with an odd number of odd degrees?

• YES

• NO

Connected and sub graphs

Isometric/Equivalent Graph

​Your text here isometric (SAME) if you move the vertices and edges without changing the number of vertices or edges and without changing which vertices the edges connect to.

Multiple Choice

Are these networks isometric?

• YES

• NO

Planar graph pg 95

Any graph that can be redrawn without overlapping lines.

Euler's Formula pg96

v = vertex

f= faces

e = edges

​v + f = e +2

Fill in the Blanks

A planar graph has four vertices and five faces.

The number of edges is ...

Hint: v + f = e + 2

Draw

A graph has the following vertices and edges:

• Vertices: A B C D E F

• Edges: (A,B),(A,C),(A,D),(A,E),(B,C),(C,D),(D,E),(E,F), (F,A)

Multiple Choice

Is the graph is planar?

Can be drawn without edges crossing

• YES

• NO

Fill in the Blanks

If it is planar, use Euler’s formula for connected planar graphs:

v + f = e +2

to calculate the number of faces.