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. 

(A) P only
(B) P and R only
(C) R only
(D) P, Q and S only


Answer: (A)

Explanation: See http://en.wikipedia.org/wiki/Line_graph

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