Homogeneoys graphs

Let Γ be a finite graph with vertex set VΓ, and let U, V be arbitrary subsets of VΓ. Γ is homogeneoys (resp. ultrahomogeneous) if whenever the induced subgraphs 〈U〉, 〈V〉 are isomorphic, some isomorphism (resp. every isomorphism) of 〈U〉 onto 〈V〉 extends to an automorphism of Γ. We extend a theorem of Sheehan on ultrahomogeneous graphs to the homogeneous case, and complete his classification of ultrahomogenous graphs.