The asymptotic number of claw-free cubic graphs Original Research Article

Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for Hn. Here we determine the asymptotic behavior of this sequence:Hn∼(2n)!e6πnn2en/3e(n/2)1/3.We have verified this formula using known asymptotic estimates of cubic graphs with loops and multiple edges and also by the method of inclusion and exclusion.