Find every simple graph g with five vertices and the

Question

Question: 1. Find every simple graph G with five vertices and the property that if exactly one edge e is added, the resulting graph G ∪e has an Eulerian circuit.

2. Consider the proposition If n is even, then n² +n is even.

(a) Prove it.

(b) State the converse.

(c) If the converse is true, prove it; if it is false, give a counter example.