We give a simple graph-theoretical proofthat the largest number ofmaximal independent vertex sets in a tree with n vertices is given by 2k+ if n 2k, m(T) 2 if n 2k + 1, a result first proved by Wilf [SIAM J. Algebraic Discrete Methods, 7 (I 986), pp. 125-130]. We also characterize those trees achieving this maximum value. Finally we investigate some related problems. Key words, independent vert...

Background: The endothelium is a monolayer of cells that extends on the vascular inner surface, responsible for the modulation of vascular tone. By means of the release of nitric oxide (NO), the endothelium has an important protective function against cardiovascular diseases. Objective: Verify if cis- [Ru(bpy)2(NO2)(NO)](PF6)2 (BPY) improves endothelial function and the sensibility of conduct...

In this paper, we study self-dual codes over the ring Z 2k of the integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings of 1 nite groups. We introduce Type II codes over Z 2k which are closely related to even unimodular lattices, as a remarkable class of self-dual codes and a generalization of binary Type II codes. A construction of even unimodula...

Ž . A Steiner minimum tree SMT in the rectilinear plane is the shortest length tree interconnecting a set of points, called the regular points, possibly using Ž . additional vertices. A k-size Steiner minimum tree kSMT is one that can be split into components where all regular points are leaves and all components have at most k leaves. The k-Steiner ratio in the rectilinear plane, r , is the in...

We prove that for position integers n, m and k, the set {1, 2, . . . , n} of integers contains k disjoint subsets having a constant sum m if and only if 2k − 1 ≤ m ≤ n(n+ 1)/(2k).