Distinct Degrees Determined by Subgraphs

We show that if a graph \(G\) has \(n\) non-isomorphic \(2\)-vertex deleted subgraphs then \(G\) has at most \(n\) distinct degrees. In addition, we prove that if \(G\) has \(3\) non-isomorphic \(3\)-vertex deleted subgraphs then \(G\) has at most \(3\) different degrees.