GATE CSE - GATE 2017-2018 Questions and Answers

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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.

P only

P and R only

R only

P, Q and S only

Answer : Option A

Explanation :

-NA-

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