Let G = (V, E) be a simple graph, with vertex set V and edge set E. A subset F ⊂ V(G) is called a decycling set if the
subgraph G−F is acyclic, that is, if G−F is a forest. The minimum cardinality of a decycling set is called the decycling number
(or feedback number) of G proposed first by Beineke and Vandell [3]. A decycling set of this cardinality is called a minimum
decycling set.