Written: May 2025

Maple packages

• TreeLine.txt, A maple package to explore Ron Graham's Tree Line Conjecture

  It also needs the data file: TreeLineData.txt .

Sample Input and Output for TreeLine.txt

• If you want to see verification of Graham's conjecture up to trees with 10 vertices
  the input gives the output

• If you want to see Graham sequence up to depth 4 for trees with vertices from 11 to 13, and depth 3 for trees with vertices from 14 to 16
  output

• If you want to see the generating function for the third entry of the Graham Line-Graph sequence for all unlabeled trees up to 16 vertices
  the input gives the output

• If you want to see the generating function for the fourth entry of the Graham Line-Graph sequence for all unlabeled trees up to 13 vertices
  the input gives the output