GATE Computer Science (CS) 2013 Solved Paper

The line graph L(G) of a simple graph G is defined as follows:

• There is exactly one vertex v(e) in L(G) for each edge e in G.
• For any two edges e and e' in G, L(G) has an edge between v(e) and v(e'), if and only if e and e' are incident with the same vertex in G.

Which of the following statements is/are TRUE?
(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.