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A064731
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Number of connected integral graphs on n vertices.
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19
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1, 1, 1, 2, 3, 6, 7, 22, 24, 83, 113, 325
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OFFSET
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1,4
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COMMENTS
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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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LINKS
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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.
K. T. Balińska, S. K. Simić, K. T. Zwierzyński, Some properties of integral graphs on 13 vertices, Tech Univ Poznań Comput Sci Cent Rep 578 (2009). This paper contains incomplete enumeration of integral graphs on 13 vertices (547), so this term is not added to the sequence at this moment.
D. Cvetkovic, S. K. Simic, Errata, Univ Beograd, Ser. Mat 15 (2004) 112.
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FORMULA
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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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Cf. A077027 (number of simple not necessarily connected integral graphs).
Cf. A287154 (number of simple disconnected integral graphs).
Cf. A363064 (number of connected Laplacian integral graphs).
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KEYWORD
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more,nonn,nice
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AUTHOR
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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 F. Royle, Dec 30 2003; confirmed by Krystyna Balinska, Apr 19 2004
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STATUS
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approved
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