The number of maximal independent sets in a connected graph

We determine the maximum number of maximal independent sets which a connected graph on n vertices can have, and we completely characterize the extremal graphs, thereby answering a question of Wilf.

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Published inDiscrete mathematics Vol. 68; no. 2; pp. 211 - 220
Main Authors Griggs, Jerrold R., Grinstead, Charles M., Guichard, David R.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1988
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Connected graph
Graph theory
Clique graph
Extremum problem
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Abstract We determine the maximum number of maximal independent sets which a connected graph on n vertices can have, and we completely characterize the extremal graphs, thereby answering a question of Wilf.
AbstractList We determine the maximum number of maximal independent sets which a connected graph on n vertices can have, and we completely characterize the extremal graphs, thereby answering a question of Wilf.
Author Griggs, Jerrold R.
Guichard, David R.
Grinstead, Charles M.
Author_xml – sequence: 1
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  surname: Griggs
  fullname: Griggs, Jerrold R.
  organization: Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A
– sequence: 2
  givenname: Charles M.
  surname: Grinstead
  fullname: Grinstead, Charles M.
  organization: Department of Mathematics, Swarthmore College, Swarthmore, PA 19081, U.S.A
– sequence: 3
  givenname: David R.
  surname: Guichard
  fullname: Guichard, David R.
  organization: Department of Mathematics, Whitman College, Walla Walla, WA 99362, U.S.A
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Cites_doi 10.1007/BF02760024
10.1137/0607015
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Issue 2
Keywords Connected graph
Graph theory
Clique graph
Extremum problem
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References B.E. Sagan, Independent sets in trees, preprint.
Z. Fűredi, The number of maximal independent sets in connected graphs, preprint.
Moon, Moser (BIB3) 1965; 3
Wilf (BIB5) 1986; 7
Harary (BIB2) 1969
10.1016/0012-365X(88)90114-8_BIB1
Wilf (10.1016/0012-365X(88)90114-8_BIB5) 1986; 7
10.1016/0012-365X(88)90114-8_BIB4
Moon (10.1016/0012-365X(88)90114-8_BIB3) 1965; 3
Harary (10.1016/0012-365X(88)90114-8_BIB2) 1969
References_xml – volume: 7
  start-page: 125
  year: 1986
  end-page: 130
  ident: BIB5
  article-title: The number of maximal independent sets in a tree
  publication-title: SIAM J. Alg. Discrete Methods
  contributor:
    fullname: Wilf
– year: 1969
  ident: BIB2
  article-title: Graph Theory
  contributor:
    fullname: Harary
– volume: 3
  start-page: 23
  year: 1965
  end-page: 28
  ident: BIB3
  article-title: On cliques in graphs
  publication-title: Israel J. Math.
  contributor:
    fullname: Moser
– volume: 3
  start-page: 23
  issue: 1
  year: 1965
  ident: 10.1016/0012-365X(88)90114-8_BIB3
  article-title: On cliques in graphs
  publication-title: Israel J. Math.
  doi: 10.1007/BF02760024
  contributor:
    fullname: Moon
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  start-page: 125
  year: 1986
  ident: 10.1016/0012-365X(88)90114-8_BIB5
  article-title: The number of maximal independent sets in a tree
  publication-title: SIAM J. Alg. Discrete Methods
  doi: 10.1137/0607015
  contributor:
    fullname: Wilf
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  ident: 10.1016/0012-365X(88)90114-8_BIB2
  contributor:
    fullname: Harary
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SubjectTerms Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Title The number of maximal independent sets in a connected graph
URI https://dx.doi.org/10.1016/0012-365X(88)90114-8
Volume 68
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