Restricted rotation distance between pairs of rooted binary trees quantifies differences in tree shape. Cleary exhibited a linear upper bound of 12n for the restricted rotation distance between two trees with n interior nodes, and a lower bound of (n − 1)/3 if the two trees satisfy a reduction condition. We obtain a significantly improved sharp upper bound of 4n− 8 for restricted rotation dista...

the effects of initial spacing layout on some allometric characteristics of 12-year-old quercus castaneifolia trees grown in central mazandaran, north of iran were examined. trees were planted in 5 different layouts (1?1, 1.5?1.5, 2?2.5, 2?3 and 4?4 m). tree height, diameter at breast height, natural pruning height and the survival of trees were recorded in each sample plot. tree basal area and...

The subtree transfer (STT) distance is one of the distance metric for comparing phylogenies. Previous work on computing the STT distance considered degree-3 trees only. In this paper, we give an approximation algorithm for the STT distance for degreed trees with arbitrary d and with generalized STT operations. Also, some NP-hardness results related to STT distance are presented.

quantifying spatial structure is one of the most important components, describing natural ecosystems and their biodiversity. in this study, a set of indices and functions related to spatial structure using 102 established plots with an area of 1000 m2 were presented. to achieve spatial structure of carpinus-fagus type, a set of indices (clark & evans, uniform angle, shannon-wiener, mingling and...

Abstract: Let G = (VG, EG) be a simple connected graph. The eccentric distance sum of G is defined as ξ(G) = ∑ v∈VG εG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v) = ∑ u∈VG dG(u, v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-...

Let G be a simple connected graph. The terminal distance matrix of G is the distance matrix between all pendant vertices of G. In this paper, we introduce some general transformations that increase the terminal distance spectral radius of a connected graph and characterize the extremal trees with respect to the terminal distance spectral radius among all trees with a fixed number of pendant ver...

1. Is there a constant ratio approximation algorithm for the nni distance on unweighted evolutionary trees or is the O(log n)-approximation the best possible? 2. Is the linear-cost subtree-transfer distance NP-hard to compute on weighted evolutionary trees if leaf labels are not allowed to be non-unique? 3. Can one improve the approximation ratio for linearcost subtree-transfer distance on weig...