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

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