Question 475379: prove that every path is gracefull.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 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
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