The line graph L(G) of a graph G has a vertex for each edge of G, and two of these vertices are adjacent iff the corresponding edges in G have a vertex in common.

a) Prove that if a simple graph G is Eulerian, then its line graph L(G) is also Eulerian.

b) Prove or disprove. The line graph of any graph is Eulerian.

c) Prove that a graph with more than two vertices of odd degree does not contain an Eulerian path (or trail).