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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