## Using the Applet

This applet will draw a subset of the complete graph on a particular number of nodes. Begin by choosing the number of nodes \(n\), a start jump value, \(a\), and an end jump value, \(b\). An edge will be drawn from node \(a\) to node \(b\). The next edge will connect \(2a\) and \(2b\), then next will connect \(3a\) and \(3b\), and so on. There may not be any connected paths in this graph. By varying the parameters, you may see the envelopes of cardioids, nephroids, and others. The possible degrees of the nodes will depend on the parameters you have chosen.

You can adjust the appearance of the graph using the options provided (colors should be entered as hex values, without a hash symbol). To watch the graph being drawn, check the Animate box and select the speed of the rendering.

Hovering over a node will highlight the edges it is connected to, and display the nodes to which it is connected.

## About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.