Reducts of the Henson graphs with a constant

Let (Hn,E) denote the Henson graph, the unique countable homogeneous graph whose age consists of all finite Kn-free graphs. In this note the reducts of the Henson graphs with a constant are determined up to first-order interdefinability. It is shown that up to first-order interdefinability (H3,E,0) has 13 reducts and (Hn,E,0) has 16 reducts for n≥4.