Prove that if $G$ contain an Eulerian circuit, then its line graph $L(G)$ also contains an Eulerian circuit.
Assume that the graph as undirected graph
then the vertice are $1,2,3,4,5,6,7$
Let $G$ be the graph with edge $(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,1)$
Apparently graph and its line graph that both will contain Eulerian circuits.
But I don't have any idea to prove it, Could you guys to help me ?