… independent vertex sets in a tree with n vertices is given by … number of maximal
independent vertex sets in a tree with n … The purpose of this note is to give a simple graph-theoretical …

… families of trees, specifically paths with auxiliary trees attached … Zhu, we show unimodality
of the independent set sequence … We also show that the independent set sequence of any tree …

… a maximum independent set. In this paper we show that maximum independent sets in trees
… to find the families of trees with the most maximum independent sets. Theorem 1 tells us that …

… Specifically, we present a novel tree representation for a general … tree. Our analysis is
algorithmic in nature, yielding a novel, tree-like, deterministic algorithm for counting independent …

… of independent sets with activity λ, where the weight of an independent set I is λ|I| … in the
weighted distribution over independent sets) on the d-regular infinite tree. We show that for d ≥ 3…

… are all lying in every maximum independent set. In this paper, we will show that if T is a tree
of order n ≥ 4 … If I is an independent set of G with cardinality , we call I an -set of G. If I is an -…

… mor independent indices of trees might be helpful. In [3] the tree o largest independent index
… Proof Since every independent set in H is an independent set in G, we have < *(G)- Let a, b …

… on trees. We first introduce a new problem-the constrained maximal independent set …
We show that, for trees, the constrained maxima1 independent set problem can be solved in …

… In this paper we consider a special case of the Maximum Weighted Independent Set
problem for graphs: given a vertex- and edgeweighted tree T = (V,E) where |V | = n, and a real …

… are obtained from independent sets of factors, and we call such independent sets canonical.
… We also give a sufficient condition for a tree T, so that T ×G has a maximum independent set …