# Subgraphs I

n =
step =

Highlight edge:

Highlight edge:

n =
step =

Highlight edge:

Highlight edge:

The subgraphs generated by this applet are created using a particular pattern. First, a trivial edge is drawn from the first node to itself. The next edge is drawn from node 1 to node \(s\), where \(s\) is the chosen skip value. Each successive edge is drawn by increasing the starting node by 1 and the ending node by \(s\). In the default example with \(s=2\), the first few edges would be \([0,0], [1,2],[2,4],[3,6],[4,8],[5,10]\) and so on.

Some envelopes that may appear include circles and cardioids, along with intricate rosettes. Other patterns include stars, grids, and combinations of several patterns.

Some envelopes that may appear include circles and cardioids, along with intricate rosettes. Other patterns include stars, grids, and combinations of several patterns.

Choose the number of nodes and a skip value. To see how the pattern is formed, increase the value of the highlighted edge. Set to 0 to turn off highlights.

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.