Answer to Question #173516 in Discrete Mathematics for ANJU JAYACHANDRAN

Question

2c) Show that any tree with exactly two vertices of degree 1 is a path.

Answer 1

Since tree (T) is a connected graph, there exist at least one path between every pair of vertices in a tree (T). Now, suppose between two vertices a and b of the tree (T) there exist two paths. The union of these two paths will contain a circuit and tree (T) cannot be a tree. Hence the above statement is proved.