Thanks Uncle Dave and Scott

So, if I have this right, the fifth is so strongly suggested by the root, that it can be left out. So does this mean there are no rootless augmented or diminished chords?

P.S. Although I am not a good musician, I did get A's in Music Theory and Music History in college. Harmony was covered, but nothing specifically for jazz. Also, one of the guitar books I worked through was Mickey Bakers Jazz Guitar, which is about it as far as my knowledge of jazz goes.

P.P.S. I like DonMs explanation of the cycle of fifths best