First off, there is no relation between number of tuples in the result of outer join and the number of ATTRIBUTES.
Assuming you meant to say that m and n denotes the number of tuples in R and S where R and S are the relations that are being full outer joined, then the minimum possible number of tuples are max(m,n) and the maximum possible number of tuples are (m+n).
Eg-
TABLE R
Table S
Here if we perform (R outer full join S) then the result will be
R FULL JOIN S
A |
B |
C |
D |
1 |
x |
NULL |
NULL |
2 |
y |
NULL |
NULL |
3 |
z |
NULL |
NULL |
NULL |
NULL |
4 |
g |
NULL |
NULL |
5 |
h |
NULL |
NULL |
6 |
i |
NULL |
NULL |
7 |
j |
This the maximum possible number of tuples that can be present in FULL JOIN, that is (m+n)
if I am mistaken please feel free to comment