We can use Alexander–Briggs notations for the links or knots. For example,
is three separate loops with no links.
And there are many other examples of Alexander–Briggs notations for three separate loops.
Question 1: where can I find the Reference and Figures for more complete lists for Alexander–Briggs notations and their corresponding graphs for three separate loops, i.e. with $$N^3_m$$ in Alexander–Briggs notations? Here $3$ means 3 separate loops. And $N$ means the crossing numbers; $m$ is simply a counting of different types.
I am interested to know, for example,
Question 2: what is $4^3_1$? and what is $5^3_1$, $4^3_2$, $5^3_2$, $6^3_4$(?) if there is any.
Note that Alexander-Briggs notation is generally reserved for prime links and so, for instance, $4_1^3$ is not usually written as any three component link with $4$ crossings (and no un-linked components) must be the connect sum of two Hopf links.
My copy of Knots and Links by Dale Rolfsen includes as an appendix the full list of prime $3$-component links with no un-linked components and up to $9$ crossings beginning at $6_1^3$ and ending at $9_{21}^3$. These links are enumerated using Alexander-Briggs notation. A bit of Googling may also find this information (I'm not sure if it would be right to link to copyrighted material).
The Handbook of Knot Theory is a good survey article for questions on enumeration and classifications of knots and links.