Minimal steiner trees on square lattices

• Main Authors: Santiago, Monique S., Ventura, Rachel P.
• Format: text
• Language: English
• Published: Animo Repository 1992
• Subjects: Trees (Graph theory); Square; Lattice theory; Graph theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16028
• Institution: De La Salle University

The paper gives a general approach in constructing minimal trees using Steiner points. Steiner points are the points added in a given set of points, used to minimize the length of the network connecting the original set of points. Such a network is called a Steiner tree. A square lattice is a set of points arranged in the form of a square. The conjectured minimal Steiner trees for square lattice of orders 2 to 14 are presented here. To construct minimal Steiner trees for square lattices of orders bigger than 14, a core square with a folded band of width 3 is used.The formulas, illustrations and theorems discussed in the thesis came from the articles, Steiner Trees on a Checkerboard by Fan Chung, Martin Gardner and Ron Graham, and Steiner minimal Trees by E. N. Gilbert and H. O. Pollack.