GATE | GATE CS 2013 | Question 26
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.