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A064731
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Number of connected integral graphs on n vertices.
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1
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1, 1, 1, 2, 3, 6, 7, 22, 24, 83, 113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| An integral graph is defined by the property that all of the eigenvalues of its adjacency matrix are integral.
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REFERENCES
| 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
| 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.
L. Wang, A survey on integral trees and integral graphs, 2005.
D. Cvetkovic, S. K. Simic, Errata, Univ Beograd, Ser. Mat 15 (2004) 112.
Eric Weisstein's World of Mathematics, Integral Graph
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EXAMPLE
| 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
| Sequence in context: A023785 A050581 A073317 * A159069 A162681 A070301
Adjacent sequences: A064728 A064729 A064730 * A064732 A064733 A064734
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KEYWORD
| more,nonn,nice
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AUTHOR
| Gordon Royle (gordon(AT)maths.uwa.edu.au), Oct 17 2001
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EXTENSIONS
| 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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