Edge-graceful Labeling - Further Selected Results

Further Selected Results

• The Petersen graph is not edge-graceful.

• The star graph (a central node and m legs of length 1) is edge-graceful when m is even and not when m is odd.

• The friendship graph is edge-graceful when m is odd and not when it is even.

• Regular trees, (depth n with each non-leaf node emitting m new vertices) are edge-graceful when m is even for any value n but not edge-graceful whenever m is odd.

• The complete graph on n vertices, is edge-graceful unless n is singly even, .

• The ladder graph is never edge-graceful.