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).

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).

Harary, F. "Covering and Packing in Graphs, I." Ann. New York Acad. Sci.175, 198-205, 1970.Harary, F.
and Palmer, E. M. Ch. 21, §P4.8 in "A Survey of Graph Enumeration
Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava).
Amsterdam: North-Holland, p. 268, 1973.Harary, F. and Palmer, E. M.
Graphical
Enumeration. New York: Academic Press, p. 225, 1973.