Suppose G is a connected graph. The block-cutpoint graph of G, BC(G) is formed as follows: Let vertices c1,c2,…,ck be the cutpoints of G, and let the blocks of G be B1,…,Bl. The vertices of BC(G) are c1,…,ck,B1,…,Bl. Add an edge {Bi,cj} if and only if cj∈Bi. Show that the block-cutpoint graph is a tree.
Note that a cutpoint is contained in at least two blocks, so that all pendant vertices of the block-cutpoint graph are blocks. These blocks are called endblocks.