The term acyclic polynomial historically denotes the matching polynomial, which encodes matchings of edges
(Gutman 1977, Farrell 1980).
Barton et al. (2022) use the term for the polynomial that counts subsets
of the vertex set inducing forests.
While they explicitly distinguish this usage from the historical meaning, the less
ambiguous and more descriptive term induced
forest polynomial is used in this work.
Barton, C.; Brown, J. I.; and Pike, D. A. "Acyclic Polynomials of Graphs." Australas. J. Combin.82, 146-181, 2022.
https://ajc.maths.uq.edu.au/pdf/82/ajc_v82_p146.pdf.Farrell,
E. J. "The Matching Polynomial and Its Relation to the Acyclic Polynomial
of a Graph." Ars Combin.9, 221-228, 1980.Gutman,
I. "The Acyclic Polynomial of a Graph." Publ. Inst. Math. (Beograd)22,
63-69, 1977.
that counts subsets
of the vertex set inducing forests.
While they explicitly distinguish this usage from the historical meaning, the less
ambiguous and more descriptive term induced
forest polynomial is used in this work.
