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
Famous quotes containing the words selected and/or results:
“The best history is but like the art of Rembrandt; it casts a vivid light on certain selected causes, on those which were best and greatest; it leaves all the rest in shadow and unseen.”
—Walter Bagehot (1826–1877)
“Nothing is as difficult as to achieve results in this world if one is filled full of great tolerance and the milk of human kindness. The person who achieves must generally be a one-ideaed individual, concentrated entirely on that one idea, and ruthless in his aspect toward other men and other ideas.”
—Corinne Roosevelt Robinson (1861–1933)