The decycling number of a graph G denoted by Δ (G), is the smallest number of vertices that can be deleted from G so that the resultant graph contains no cycles. The cycle packing number of a graph G denoted byc(G), is the maximum number of vertex disjoint cycles in G. It is clear that c(G)≤.Δ(G) We find certain networks for which decycling number equals the cycle packing number. © 2015 The Authors. Published by Elsevier B.V.