show that if two trees have isomorphic line graphs , they are isomorphic.

Question

i want to use Whitney isomorphism theorem : if the line graphs of two connected graphs are isomorphic , then the underlying graphs are isomorphic. except in the case of the triangle graph K3 and K1,3 , which have isomorphic line graphs but are not themselves isomorphic. whitney's theorem will work here since the trees are connected graphs , but where can I find a proof of Whitney's isomorphism theorem. any suggestion would be appreciated.

Answer 1

Harary's "Graph Theory" book has a chapter on line graphs (see Chapter 8), where Whitney's isomorphism theorem (Theorem 8.3) is proved.