  (Solution) 18. If G _ (V , E) Is An Undirected Loop-free Graph, The Line Graph OfG, Denoted L(G), Is A Graph With The Set E As Vertices, Where We Join Two | Snapessays.com

(Solution) 18. If G _ (V , E) is an undirected loop-free graph, the line graph ofG, denoted L(G), is a graph with the set E as vertices, where we join two

18. If G _ (V , E) is an undirected loop-free graph, the line

graph ofG, denoted L(G), is a graph with the set E as vertices,

where we join two vertices e1, e2 in L(G) if and only if e1, e2

are adjacent edges in G.

a) Find L(G) for each of the graphs in Fig. 11.99.

b) Assuming that |V | _ n and |E| _ e, show that L(G)

has e vertices and (1/2)

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