Trees with extremal numbers of maximal independent sets including the set of leaves |
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Authors: | Iwona W?och |
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Institution: | Faculty of Mathematics and Applied Physics, Technical University of Rzeszów, ul.W.Pola 2, 35-959 Rzeszów, Poland |
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Abstract: | A subset S of vertices of a graph G is independent if no two vertices in S are adjacent. In this paper we study maximal (with respect to set inclusion) independent sets in trees including the set of leaves. In particular the smallest and the largest number of these sets among n-vertex trees are determined characterizing corresponding trees. We define a local augmentation of trees that preserves the number of maximal independent sets including the set of leaves. |
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Keywords: | 05C69 05C05 |
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