The number of maximal independent sets in a connected graph
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The maximum number of maximal independent sets which a connected graph on n vertices can have is determined, and the extremal graphs are completely characterize, thereby answering a question of Wilf.About:
This article is published in Discrete Mathematics.The article was published on 1988-02-01 and is currently open access. It has received 92 citations till now. The article focuses on the topics: Maximal independent set & Independent set.read more
Citations
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The number of maximal independent sets of (k + 1)-valent trees
TL;DR: In this article, the authors classify maximal independent sets of (k + 1)-valent trees into two groups, namely, type A and type B, and study relations among these three types of independent sets.
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Maximal independent sets in clique-free graphs
TL;DR: In this paper, the maximum number of maximal independent sets (MISs) of size (n/k) in an n-vertex graph can be asymptotic to the extremal construction of a disjoint union of k-cliques with sizes as close to n/k$ as possible.
References
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On cliques in graphs
J. W. Moon,L. Moser +1 more
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
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The number of maximal independent sets in a tree
TL;DR: In this paper, the maximal independent sets of vertices that any tree of n vertices can have were shown to have maximal number of maximal independent vertices, where vertices are independent sets.
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The number of maximal independent sets in connected graphs
TL;DR: A theorem of Moon and Moser is generalized to determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50.