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A129581
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Number of labeled prime graphs with respect to the Cartesian multiplication of graphs.
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0
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1, 1, 4, 35, 728, 26464, 1866256, 251518352, 66296210432, 34496477587456, 35641657548953344, 73354596197458024448, 301272202649664088951808, 2471648811030427594714599424, 40527680937730480229320939012096
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Ji Li, Prime graphs and exponential Composition of Species, arXiv:0705.0038
Ji Li, Prime graphs and exponential composition of species, J. Combin. Theory A 115 (2008) 1374-1401
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FORMULA
| Let D(P) be the exponential Dirichlet generating series for the species of prime graphs and let D(C) be the exponential Dirichlet generating series for the species of connected graphs. We have D(P)=log D(C)
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EXAMPLE
| Almost all connected graphs are prime graphs with respect to Cartesian product of graphs. So instead of giving an example of prime graph, we give here an example of a connected nonprime graph on vertices {1,2,3,4}:
1 --- 4
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2 --- 3
The above graph is not prime since it is the Cartesian product of two line graphs of order 2.
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CROSSREFS
| Cf. This is the logarithmic of A001187. Unlabeled prime graphs is given by A129582.
Sequence in context: A005973 A007134 A125798 * A120055 A192012 A076818
Adjacent sequences: A129578 A129579 A129580 * A129582 A129583 A129584
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KEYWORD
| easy,nonn
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AUTHOR
| Ji Li (vieplivee(AT)hotmail.com), May 04 2007
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