image Information file for Petersen.

To install Petersen:

  1. If you obtained the installation files as a zip file first unzip it.
  2. Run the file called "setup.exe". (You can also use the Add/Remove programs option in the control panel.)
  3. 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
  1. Obtain G1and save it.
  2. Obtain G2.
  3. Select Relations and Isomorphism from the menu.
  4. 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.
  5. 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
  1. Obtain G1and save it.
  2. Obtain G2.
  3. Select Operations and Union from the menu.
  4. You will get a dialog box asking you to select the second graph. The graph G1 will be one of the choices. Select it.
  5. 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:
  1. Select Picture and then Weights and then On
  2. Get a Null graph with the number of vertices you need by selecting Graph and then Null Graph
  3. 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:
  1. Check that the weights option is on (Select Picture and then Weights and then On)
  2. Erase the edge by drawing over it with the RIGHT mouse.
  3. 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