# The line graph lg of a simple graph g is defined as

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13. 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.
Tutorial_10 Graph Theory 4 Common Data for Questions 14 and 15: Consider a complete undirected graph with vertex set {01,2,3,4} V . Entry ij W in the matrix W below is the weight of the edge { , } i j . 0 1 8 1 4 1 0 12 4 9 8 12 0 7 3 1 4 7 0 2 4 9 3 2 0 W
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