Steiner trees and spanning trees in six-pin soap films

Steiner trees and spanning trees in six-pin soap films

Abstract We have studied the Steiner tree problem using six-pin soap films in detail. We extend the existing method of experimental realisation of Steiner trees in n-terminal problem through soap films to observe new non-minimal Steiner trees. We also produced spanning tree configurations for the first time by our method. Experimentally, by varying the pin diameter, we have achieved these new s...

On Steiner trees and minimum spanning trees in hypergraphs

Rotationally optimal spanning and Steiner trees in uniform orientation metrics

We consider the problem of finding a minimum spanning and Steiner tree for a set of points in the plane where the orientations of edge segments are restricted to uniformly distributed orientations, , and where the coordinate system can be rotated around the origin by an arbitrary angle. The most important cases with applications in VLSI design arise when or . In the former, so-called rectilinea...

Spanning Trees in 2-trees

A spanning tree of a graph G is a connected acyclic spanning subgraph of G. We consider enumeration of spanning trees when G is a 2-tree, meaning that G is obtained from one edge by iteratively adding a vertex whose neighborhood consists of two adjacent vertices. We use this construction order both to inductively list the spanning trees without repetition and to give bounds on the number of the...

Effects of Liquid Soap and Dishwashing Detergent on Pistachio Trees

The common pistachio psyllid, Agonoscena pistaciae Burckhardt and Lauterer (Hemiptera: Aphalaridae) is the key pest of pistachio trees in Iran. Nowadays, pistachio growers use detergents widely to control this pest in pistachio orchards. Consequently, the study was carried out to investigate the effects of applying liquid soap (Jonobgan®) 3500 ppm, dishwashing deter...