# Samuel Vidal

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 Name Samuel Vidal Member for 1 year Seen Mar 31 at 14:21 Website Location Paris Age 31
 Feb24 answered Nth root of a matrix as an analytic function? Feb9 comment Is the empty graph a tree?"disconnected" and "connected" not forming a dichotomy : brilliant, that's the point ! Feb9 comment What is the cardinality of the family of unlabelled bipartite graphs on n vertices?thank you sir ! Feb5 answered What is the cardinality of the family of unlabelled bipartite graphs on n vertices? Feb5 comment What is the cardinality of the family of unlabelled bipartite graphs on n vertices?I've checked the combinatorial description which is ok (the isomorphisms of species) The computation is wrong and I 'm not sure how to do it right. There is a description of the functorial composition of species in the book on species but it is hard to work out. Feb3 revised What is the cardinality of the family of unlabelled bipartite graphs on n vertices?added 333 characters in body Feb3 answered What is the cardinality of the family of unlabelled bipartite graphs on n vertices? Feb3 comment Is the empty graph a tree?May be a way to clarify the question is to consider not the graph in itself but within its family. Consider The family (species) of connected graphs $G^c$ and the family of not necessarily connected graphs $G$. The relation between them is: $$G\simeq E(G^c)$$ where E stands for the species of sets. This natural isomorphism comes from existence and unicity of a decomposition of a graph (in $G$) in its connected components (in $G^c$). If you work out the details, $G^c$ can't have any graph of size zero. This is why you better not see the empty graph as connected. Feb1 revised Is the empty graph a tree?deleted 11 characters in body Feb1 answered Is the empty graph a tree?