ground of Arduino and ground of power source

Rochas:
sorry that I didn't explain it clearly. Attached are the two circuits that I plan on using (sorry that I don't have software for this kind of drawing). Just not sure which grounding scheme is more appropriate. The first scheme treats the input to uno (reducing source power volt) and the output from uno as two circuits; the second one lumps them together. I worry that the 2nd one might accidentally feed undesired currently back to the power source (which will potentially blow the power source) if the relative voltage of uno ground is different from the ground of 7805. But I am not sure if scheme 1 is grounded sufficiently. Or maybe the basic design has some fundamental flaw?? Any suggestion will be greatly appreciated.

Well that is also confusing for different reasons. The polarity of you external power supply as wired to the 7805 appears to be ok, however you don't have the common side of the power supply (what you call -28) wired to a arduino ground pin, and that is required.

But also I don't understand why you have a jumper wire connecting what you call output (an output pin?) connected to a arduino ground pin? If that is the case if you ever set the output pin to a high (+5vdc) it would be a direct short to the arduino ground pin, which would destroy the output pin. So the wire you labeled with a ? is correct in the second drawing, but again both drawings show a jumper wire from arduino ground to something labled output, which is most certainly incorrect as stated before.

Lefty