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A129581
Number of labeled prime graphs with respect to the Cartesian multiplication of graphs.
0
1, 1, 4, 35, 728, 26464, 1866256, 251518352, 66296210432, 34496477587456, 35641657548953344, 73354596197458024448, 301272202649664088951808, 2471648811030427594714599424, 40527680937730480229320939012096
OFFSET
1,3
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)
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
| ... |
2 --- 3
The above graph is not prime since it is the Cartesian product of two line graphs of order 2.
CROSSREFS
Cf. This is the logarithmic of A001187. Unlabeled prime graphs is given by A129582.
Sequence in context: A376111 A351730 A125798 * A371633 A356544 A120055
KEYWORD
easy,nonn
AUTHOR
Ji Li (vieplivee(AT)hotmail.com), May 04 2007
STATUS
approved