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.
Read more about this topic: Edge-graceful Labeling
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