OFFSET
1,3
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
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
KEYWORD
easy,nonn
AUTHOR
Ji Li (vieplivee(AT)hotmail.com), May 04 2007
STATUS
approved