Let G be a simple graph with
30 vertices of degree 1,
6 vertices of degree 2,
5 vertices of degree 3,
2 vertices of degree 4 and
1 vertex of degree 5.
Additionally, assume G doesn't contain any cycles, and has no vertices of any other degree. How many connected components does G have?
I know there are 44 vertices and n−1 edges in a tree, which would be 43 edges. So would the amount of connected components in G be 1?
