We introduce a new technique to associate a spanning tree to the average linkage cluster analysis. We term this tree as the Average Linkage Minimum Spanning Tree. We also introduce a technique to associate a value of reliability to links of correlation based graphs by using bootstrap replicas of data. Both techniques are applied to the portfolio of the 300 most capitalized stocks traded at New ...

Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those metho...

The problem of grouping the gray value variations at the border of complex structured surfaces in outdoor scenes is considered in order to get a simple symbolic representation of such boundaries. Our approach is based on a combination of histogram und minimal spanning tree (a graph-theoretical method) evaluation. In this way the direction and magnitude of the gray value gradient and additionall...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimal possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. Du et al. (1993) conjectured that the Steiner ratio on a normed plan...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the ,metric space. In this note, we show that for any Minkowski plane, the Steiner rat...

The Rooted Distance-Constrained Minimum Spanning Tree Problem (RDMSTP) is defined as follows: given a graph G = (V,E) with node set V = {0,1,...,n} and edge set E, two integer weights, a cost ce and a delay we associated with each edge e of E, and a natural (time limit) number H, we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specifie...