The Domination Number of Cubic Graphs with Girth at least Five

Let γ (G) be the domination number of a graph G. We show that if G has maximum degree at most 3 and girth at least 5, then γ(G) ≤ 17(4n − e + p + 3i) where G has n nodes, e edges, p pendant nodes, and i isolated nodes. It follows that if G is a cubic graph with girth at least 5, then γ (G) ≤ 514n.