# Subgraphs I

n =     step =

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.

## Using the Applet

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.