vs. or vs for versus

If an abbreviation consists of the first and last letters of a word (e.g. 'vs' for the Latin word versus, Dr for Doctor, Mr for Mister, St for Saint and so on), the American rule is to include a full/stop period at the end. The British norm, however, is not to use a period at the end.

...tho many of us Yanks lean to the Brit

Following this rule, I conclude I should include a period after 'etc.', as it does not consist of the first and last letter of et cetera.
However, Longman Dictionary of Contemporary English writes:
etc. (also etc British English)

I am a little bit confused now.

Decide whether you are writing British English or American English. If British, do not follow etc with a period. If American, use a period.

But there is a common rule in British English (you even told me that): If an abbreviation consists of the first and last letters of a word, a period is normally omitted. If the abbreviation consists only of the first part of a word, then you should put a period at the end.

So to me, abbreviations like 'Prof.' or 'etc.' are written correctly that way.

So use the period. I

To complicate matters ('cause I'm a stinker), at least in America, lawyers and judges just use v.

As in:
Brown v. Board of Education