Given a tree T, let q(T) be the minimum number of distinct eigenvalues in symmetric matrix whose underlying graph is T. It well known that q(T)≥d(T)+1, where d(T) diameter and T said to diminimal if q(T)=d(T)+1. In this paper, we present families trees any fixed diameter. Our proof constructive, allowing us compute, for d these families, M with spectrum has exactly d+1 eigenvalues.

In order to determine the best form factor formula for Loblolly Pine (Pinus taeda L.) plantations in Talesh (Western Guilan province-Iran), a number of 110 trees were selected based on their distribution in diameter classes, from 12 to 34 cm (in a two- cm diameter interval). First, several quantitative factors including diameter at breast height, diameter at 0.65 m of height, and diameter at st...

Variation in angiosperm vessel diameter is of major functional significance. In the light of recent models predicting optimal vessel taper given resistance imposed by conductive path length, we tested the prediction that plant size should predict vessel diameter, with dryland plants having narrower vessels for their stem sizes. We assembled a comparative dataset including vessel and stem diamet...