Discussion:
Q: A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way that the induced edge labeling, which assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G. The graceful tree conjecture states that every tree is graceful.
a. Prove that every path is graceful.
b. Prove that every star K_(1,n) is graceful.
c. Show that every tree of order 6 is graceful.