A connected simple graph G has 14 vertices and 88 edges. Prove G is not Eulerian. A connected simple graph G has 14 vertices and 88 edges. Prove G is not Eulerian.
-This was a two part question, and for the first part I had to prove why the graph is Hamiltonian, but now i am struggling with proving why it is not Eularian. The hint my teacher gave me was to prove that G has at least 8 vertices of degree 13, which I unfortunately still can't solve, any help is appreciated.

Step 1: prove the hint.  Suppose it's not true, then bound the total number of edges by bounding the edges at each vertex, and get a contradiction.
Step 2: Since $8>2$, there are more than two vertices of odd degree.
Step 3: Profit.
