R. C. Read defined the anarboricity of a graph 
as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of 
whose union is 
(Harary and Palmer 1973, p. 268).
Anarboricity is therefore defined only for cyclic graphs. It equals 1 for a unicyclic graph (since the only cyclic subgraph from which the original graph can be constructed is the entire graph).
By construction, the Dutch windmill graph 
has anarboricity 
, and the special case of the butterfly
graph 
has anarboricity 2.
The term "anarboricity" is a "glorious groaning pun" (in the words of Harary and Palmer 1973, p. 268) on the city of Ann Arbor (the location of the main campus of the University of Michigan).
