Graph Creator

Choose Draw > Vertex, or highlight the circle image along the left side, to be able to add vertices to the graph. Then, click on the drawing space to place vertices.

Choose Draw > Edge, or highlight the line segment image along the left side, to be able to add edges to the graph. Then, click-and-drag between two vertices to connect them with an edge.

Choose Draw > Select, or highlight the arrow image along the left side, to be able to select pieces of the graph. By using the select tool to identify a rectangular region, all items within that region will be selected.

Vertices can be moved within the drawing space. A major benefit of this tool is that the endpoint of edges connected to a vertex are moved when the vertex is moved.

Create four vertices, and connect all possible pairs of vertices with an edge. (In total, there will be six edges.)

• Can you move some of the vertices so that the edges intersect only at the vertices? That is, can this graph be drawn so that none of the edges intersect one another?
• A graph is said to be planar if it can be drawn on a plane so that the edges intersect only at the vertices. Is this graph planar?

 

Create five vertices, and connect all possible pairs of vertices with an edge. (In total, there will be ten edges.)

• Is this graph planar?
• What is the fewest number of edges you would need to remove so that the resulting graph would be planar?