##### For an undirected graph G = (V,E), the line graph G = (V , E ) is obtained by replacing

For an undirected graph G = (V,E), the line graph G = (V , E ) is obtained by replacing each edge in E by a vertex, and adding an edge between two vertices in V if the corresponding edges in G are incident on the same vertex. Which of the following is TRUE of line graphs?

(A) the line graph for a complete graph is complete

(B) the line graph for a connected graph is connected

(C) the line graph for a bipartite graph is bipartite

(D) each vertex in the line graph has degree one or two

Answer: B