Information
file for Petersen.
To install Petersen:
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If you obtained the installation files as a zip file
first unzip it.
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Run the file called "setup.exe". (You can also use
the Add/Remove programs option in the control panel.)
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The installation wizard will guide you through the
installation process. Once the program has been installed, its icon will
appear in a group called Petersen.
Basic Information:
Note that this software uses both the right and
left mouse buttons.
To add a vertex:
Select Edit and then Add Vertex. A
new vertex will appear in the top left corner of the screen.
To remove a vertex:
Select Edit and then Remove Vertex.
You will be asked which vertex to remove. The vertices will be re-labeled
to reflect the change.
To move a vertex:
With the mouse on the vertex, press the LEFT
mouse button and drag the vertex to the new location. [If the whole graph
moves rather than just the vertex then select
Picture and Move
Graph to remove the check mark on that menu item.]
To add an edge from one vertex to another:
With the mouse over one of the vertices press the
RIGHT mouse button and draw (drag the mouse) to the second vertex.
To merge two vertices:
Select Edit and then Merge Vertices.
You will be asked which vertices to merge. Note the vertices will be re-labeled
to reflect the change.
To move the graph:
Select Picture and then Move Graph.
Now if you drag any vertex to a new location using the LEFT mouse, the
whole graph will follow. Select Picture and Move Graph again
to get back the default behavior.
To center the graph on the screen:
Select Picture and then Center.
To save a graph:
Select the Graph and then the Save
menu items. You can save up to 20 graphs.
To restore a saved graph:
Select the Graph and then the Restore
menu item. Select the graph you want to restore and click OK.
To get a named graph:
Select the Graph menu item. From the choices
you can select the appropriate graph.
To draw your own graph:
It is easiest to start with a null graph with the
number of vertices you need and then draw in the edges and move the vertices
to the locations you want them to be in.
To change the title:
The title is a useful way to refer to the graph.
To change the title of the graph select
Picture and then Change
Title from the menu.
To switch the color on and off:
The reason we use many colors is so that the vertex
and its label can have the same color which makes it easier to keep track
of which label belongs to which vertex. If you wish to have a black and
white picture you can turn off the color by selecting Picture and then
Color and then Off. from the menu.
To change the thickness of the edges and size of
the vertices:
Select Picture and then Line width.
Note that a line width of 0 gives you a little square that you can move
around. Only the labels appear in that square. if you have a very crowded
graph this make it easier to identify the vertices this can be useful.
To change the size of the graph:
Select Picture and then Size.
To rotate the graph:
Select Picture, then select Flip Graph
and then Rotate. In the dialog box enter the number of degrees through
which you want to rotate the graph.
To swap the labels of two vertices:
Select Edit and then Swap Labels. You
will be asked which vertices should have their labels swapped. The vertices
will be re-labeled to reflect the change.
To get basic statistics for the graph:
Select Properties and then Statistics
If you wish you print them select Print from the menu.
To get adjacency matrix a graph:
Select Properties and then
Adjacency Matrix. If it is a large graph you might have
to click on the More button to see more of the matrix.
To find the number of connected components:
Select Properties and then Components. The
components will be listed at the bottom of the screen.
To break the graph up visually into its components:
Select
Edit and then Show Components.
To find a Hamilton circuit:
Select Properties and then Hamilton Circuit
The circuit (if there is one) will be traced out on the graph. To speed
up or slow down the animation use the buttons at the bottom right of the
screen.
To find an Euler circuit:
Select Properties and then Euler Circuit.
The circuit (if there is one) will be traced out on the graph. To speed
up or slow down the animation use the buttons at the bottom right of the
screen.
To find the chromatic number of a graph:
Select Properties and then Chromatic number.
To find the articulation points of a graph:
Select Properties and then Articulation
Points.
To check if a graph is bipartite:
Select Properties and then Bipartite?.
To count the number of regions in a planar graph:
The software has algorithms for counting the number
of regions of a plane depiction of a graph and also for finding the dual
graph. The algorithms only work on graphs with no bridges. To get to these
features select Properties and then Planar Graphs
Isomorphism:
The software can check for isomorphism between the
graph currently displayed and a graph previously saved. Therefore to check
if graph G1 is isomorphic to graph G2
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Obtain G1and save it.
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Obtain G2.
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Select Relations and Isomorphism from
the menu.
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Click on the Start button and you will get a dialog
box asking you to select the second graph. The graph G1
will be one of the choices. Select it.
-
You will see a message in the test box telling you
if the two graphs are isomorphic. If they are you can click on the Morph
button to get some animation.
Subgraphs:
The procedure to check if graph G1
is isomorphic to graph G2 is identical to the one for
isomorphism except that you use the Find Subgraph menu item on the
Relations menu.
Complements:
To get the complement of a graph select
Operations
and then Complement.
Line Graphs:
To get the line graph of a graph select
Operations
and then Line Graph.
Prisms:
To get the prism of a graph select
Operations
and then Prism.
Unions:
To obtain the union of a graph G1
and a graph G2
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Obtain G1and save it.
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Obtain G2.
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Select Operations and Union from the
menu.
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You will get a dialog box asking you to select the
second graph. The graph G1 will be one of the choices.
Select it.
-
You will get the union of the two graphs.
Sums:
The procedure to obtain the sum of a graph G1
and a graph G2 is identical to the one for unions except
that you use the Sum menu item on the Operations menu.
Searches:
The software demonstrates breadth first and depth
first searches in connected graphs. The demonstrate a search select Find,
Search, and then either Breadth First or Depth First.
To draw a weighted graph:
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Select Picture and then Weights and
then On
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Get a Null graph with the number of vertices you
need by selecting Graph and then Null Graph
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Draw in you edges by dragging the RIGHT mouse
from vertex to vertex. Each time you draw an edge you will be asked for
the weight for that edge. To erase an edge you just draw over it with the
RIGHT mouse again.
To change the weight of an edge:
-
Check that the weights option is on (Select Picture
and then Weights and then On)
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Erase the edge by drawing over it with the RIGHT
mouse.
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Draw the edge in again (drag with the RIGHT
mouse). You will be asked to input the weight of the edge.
To assign weights at random:
Select Picture and then Weights and
then Assign. Weights ranging from 1 to 100 will be assigned at random
to the edges.
Shortest Path:
To find the shortest path between two vertices using
Dijstra's algorithm Find, Shortest Path, and then
Dijstra.
Spanning Trees:
The software demonstrates breadth first and depth
first spanning trees. If you select Find and then Spanning Tree
you can then select either Breadth First or Depth First.
Minimum Spanning Trees:
The software demonstrates Kruskal's algorithm and
Prim's algorithm for finding minimal spanning trees. Select Find
and then Spanning Tree and then Min Span Tree and then you
can then select either Kruskal or Prim.
© C. Mawata