Multiple choice

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.

  1. P only

  2. P and R only

  3. R only

  4. P, Q and S only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P) The line graph of a cycle is a cycle.

R) Line graph of planar graph is planar.

S)

The line graph of a tree need not be tree.

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