Question 475379
Label a path with three vertices:


1--3--2


A path with four vertices:


1--4--2--3


A path with five vertices:


1--5--2--4--3


In general, label an n-sided graph with the numbers 1, n, 2, n-1, 3, n-2,..., in which the differences between consecutive nodes are n-1, n-2, ..., 1, hence, graceful.


The following website gives more information about graceful graphs:
http://mathworld.wolfram.com/GracefulGraph.html