Minimal trees of given search number
β Scribed by Jonathan D.H. Smith
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 717 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A recurrence relation and asymptotic estimate for the number of minimal trees of given search number are derived. In addition, a language for describing these trees and structures within them is developed. Their automorphisms groups are also discussed.
π SIMILAR VOLUMES
Steiner minimal tree for a given set of points in the plane is a tree which interconnects these points using Eines of shortest possible total length. We construct an infinite class of trees which are the unique full Steiner minimal trees for their sets of endpoints (vertices of degree one).
We show that any tree that has a universal minimal total dominating function has one which only takes 0-1 values. K 3 demonstrates that this fails for graphs in general. Given a graph G =(V, E), for each vertex ve V let F(v) be the set of its neighbours (in particular, not including v itself). A to