Manual
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Graph
You can generate four types of graphs:
- the empty graph
- the double n-fan
- the n-cycle
- the (nxn)-grid
Just input the desired size n and hit "new graph".
Modes
The program operates in four modes:
- Construct
- Change the graph by creating and deleting nodes and edges.
- Rearrange
- Drag nodes around.
- Local Pivot
- Take local complements and edge pivots. Move the mouse over a vertex or edge to see the associated operation highlighted (green edges are added, red edges are removed). Clicking a vertex or edge executes the highlighted changes. For edge pivots the end vertices of the selected edge are swapped (and the changes arising from this are not highlighted).
- General Pivot
- Take pivots with general vertex sets. Draw frames to XOR with the current selection and hit the "execute pivot" button to apply the highlighted changes. If the selected nodes turn orange, then the corresponding submatrix of the adjacency matrix is singular and no pivot operation is possible. The cut-rank of the selected vertex set is shown on the left.
History
Keeps a log of the things you did, so that you always can look up how you got from one graph to another. The log is reset when creating a new graph by hitting "new graph". The display of node labels and the adjacency matrix can be toggled here. Hit "save" or "restore" to save or restore the current graph, including the log. The "minimising move" button finds the local complements and edge pivots that get rid of as many edges as possible and highlights them (in red).