It's in the SECNAV Correspondence Manual, M-5216.5, IIRC.
It's V/r, because it's Sentence case not Title Case: Very respectfully, is shortened to V/r,
When speaking to equal or lower rank it's Respectfully, or R,
The SECNAV manual will tell you that the abbreviations are only for follow-on conversations within an email chain. Initial emails should be spelled out, but almost no one does that.
OTOH, everyone thoughtlessly uses R/ per the manual, even though Respectfully, would be abbreviated as R,
I submitted a change request to fix it, but I think it was ignored. (Yes. I'm a huge nerd.)