2.8 Degrees & Isomorphism

Non-Isomorphic Graphs

Let's call the graph on the left \(G \) and the graph on the right \(H \). The two graphs are not isomorphic. Indicate which of the following assertions can prove this fact.

Exercise 1

Note that the last assertion mentions properties that are preserved under isomorphism, and so if it were true, it could prove that \(G\) and \(H\) are not isomorphic. Unfortunately, this assertion isn't true; both graphs actually have an edge that is incident to two vertices of degree 3.