What type of graph problem is this? Lets say I have four group
A [ 0, 4, 9]
B [ 2, 6, 11]
C [ 3, 8, 13]
D [ 7, 12 ]
Now I need a number from each group(i.e a new group) E [num in A,num in B, num in C, num in D], such that the difference between the maximum num in E and minimum num in E should be possible lowest.What type of problem is this ? which graph algorithm will be better to solve this kind of problem ? 
Thanks in advance.
 A: I can't think of any reasonable way to represent this problem using
graphs.
I suggest the following to deal with your problem: 
1) keep the elements of each groups sorted .
denote $n$ as the total number of elements ($n=|A|+...+|D|)$, for
each $M\in\{A,B,C,D\}$ denote$U_{M}$ as the union of the other groups
with higher alphabetical order (for example $U_{B}=C\cup D)$.
2) since we have to choose one element from each group we have to
choose one from $M$, for every element in $M$ find an element in$U_{M}$
s.t the difference is minimal (since the elements are sorted you can
do this in $log(|U|)$ using binary search).
save this minimum in
a variable and update it when you find a new minimum (also save the
elements that gave you the minimum and the groups they came from so
you can know what elements in what groups give this minimum)
At the end of this procedure you will know what two elements in which
groups give you your minimum, of course you can take the other two
elements for $E$ in an arbitrary way without it affecting the minimum.
The time complexity is $O(nlog(n))$ since for every $M$ it holds
that $|M|\leq n$ and$|U_{M}|\leq n$.
