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Search: id:A064731
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| A064731 |
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Number of connected integral graphs on n vertices. |
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+0
2
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| 1, 1, 1, 2, 3, 6, 7, 22, 24, 83, 113
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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An integral graph is defined by the property that all of the eigenvalues of its adjacency matrix are integral.
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REFERENCES
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K. Balinska, D. Cvetkovic, Z. Radosavljevic, S. Simic and D. Stevanovic, A survey of integral graphs, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 42-65. However, the values given there for a(11) and a(12) are incorrect.
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LINKS
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K. Balinska, D. Cvetkovic, Z. Radosavljevic, S. Simic and D. Stevanovic, A survey of integral graphs. However, the values given there for a(11) and a(12) are incorrect.
Eric Weisstein's World of Mathematics, Integral Graph
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EXAMPLE
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The three integral graphs on five vertices are the star K1,4, the complete graph K5 and the complete join (K2 join 3K1).
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CROSSREFS
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Sequence in context: A023785 A050581 A073317 this_sequence A159069 A162681 A070301
Adjacent sequences: A064728 A064729 A064730 this_sequence A064732 A064733 A064734
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KEYWORD
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more,nonn,nice
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AUTHOR
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Gordon Royle (gordon(AT)maths.uwa.edu.au), Oct 17 2001
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EXTENSIONS
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a(11) = 236 and a(12) = 325 (from the BCRSS paper) sent by Felix Goldberg (felixg(AT)tx.technion.ac.il), Oct 06 2003. However, it appears that those numbers were incorrect.
a(11) = 113 from Gordon Royle, Dec 30, 2003. Confirmed by Krystyna Balinska, Apr 19 2004.
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