A distributed algorithm for finding minimal feedback vertex sets in directed split-stars

In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G)/F is acyclic. In this paper, we propose an algorithm for finding minimal feedback vertex sets of directed split-stars. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for directed split-stars. Moreover, a simple distributed algorithm is presented for finding such sets.