There's some discussion at What is the correct abbreviation for the word "numbers"? about the use of the abbreviation "No." for "number". However, my question is about the necessity of writing "of" after "no." when abbreviating "number of [foo]".
Question: Should one use "of" when abbreviating "number of…" using "no."?
As a concrete example,
Number of queries
could be abbreviated in one of these two ways:
No. queries
No. of queries
I'm accustomed to e.g. "Proceedings of the National Academy of Science of the United States of America" being abbreviated "Proc. Natl. Acad. Sci. U.S.A.", but this might be limited to journal abbreviations.
In my particular situation, I am abbreviating an axis label on a figure, and using an unabbreviated version in the caption.
One of the answers to the above question writes e.g. "Number of guests" should not be abbreviated, although it's a common enough abbreviation in computer science; examples can be found by searching for "No. of queries" in Google Scholar.
Best Answer
Your issue may arise from the etymology of № vs. 'no.':
The Oxford English Dictionary derives the numero sign from Latin numero, the ablative form of numerus ("number", with the ablative denotations of: "by the number, with the number").
In American English, the hash mark tends to be used to denote numero instead of №, which also add to the confusion.
Unfortunately, due to the rise of keyboards, the sign '№' has fallen out of use, with its typographical alternative becoming no[.]. This then creates a conflict between the abbreviation no. meaning number (from French nombre) and № (from the Latin numero).1
Back to the question - Since it is common to use the abbreviation 'no.' to mean number of, particularly in technical circumstances such as yours, it seems perfectly appropriate to abbreviate it as you have. I would usually warn that you might want to use the unabbreviated form in a caption or article but I see you already have.
Footnotes:
1: It is, of course, unfortunate that both the French and Latin come from the same Latin word numerus, but hey, that's language!