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A064731 Number of connected integral graphs on n vertices. +0
2
1, 1, 1, 2, 3, 6, 7, 22, 24, 83, 113 (list; graph; listen)
OFFSET

1,4

COMMENT

An integral graph is defined by the property that all of the eigenvalues of its adjacency matrix are integral.

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.

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.

Eric Weisstein's World of Mathematics, Integral Graph

EXAMPLE

The three integral graphs on five vertices are the star K1,4, the complete graph K5 and the complete join (K2 join 3K1).

CROSSREFS

Adjacent sequences: A064728 A064729 A064730 this_sequence A064732 A064733 A064734

Sequence in context: A023785 A050581 A073317 this_sequence A070301 A065536 A088414

KEYWORD

more,nonn,nice

AUTHOR

Gordon Royle (gordon(AT)cs.uwa.edu.au), Oct 17 2001

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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Last modified October 11 09:12 EDT 2008. Contains 144832 sequences.


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