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
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Coverings, Matchings and the number of maximal independent sets of graphs
Do Trong Hoang,Tran Nam Trung +1 more
TL;DR: The maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers is determined and the extremal graphs are completely characterize.
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The number of maximal independent sets in trees with a given number of leaves
TL;DR: For any n and l, the authors describes trees with the maximum and minimum number of maximal independent sets among all n-vertex trees with l leaves, for any n ≥ 2.
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Network-Coded Macrocell Offloading in Femtocaching-Assisted Cellular Networks
TL;DR: In this paper, the authors proposed an ONC-broadcast scheme that exploits both broadcasting and opportunistic network coding (ONC) to minimize the number of required MBS transmissions.
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On the maximum number of maximum independent sets in connected graphs
Elena Mohr,Dieter Rautenbach +1 more
TL;DR: In this article, the authors characterize the connected graphs of given order n and given independence number α that maximize the number of maximum independent sets of a given graph. But they do not characterize the graphs that arise from the disjoint union of cliques of orders n and α.
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Difficult Problems in Threshold Graphs
TL;DR: This work uses a structural characterization of threshold graphs for solving difficult problems: enumerating all the maximal independent sets and the chromatic index problem.
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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.