Given a list of vertices associated with its degree, says: $$7, 7, 3, 3, 3, 3, 3, 1$$ Determine whether it is possible to draw a graph $G$, where $G$ is connected and un-directed.
Solution: The above graph is impossible to draw because the first two vertices will make every other vertices have degree 2.
But I realize this approach is too specific, and it's not feasible if the given list is large, let's say $n > 100$, where $n$ is the number of vertices. So my question is, if a general list of $n$ vertices is given with a degree from $1 \rightarrow n - 1$, then is there a general formula to determine whether it is possible to draw its graph? Thank you.