How many graphs is there, with 5 vertices and 3 edges of maximum degree 3?
I don't know if that graph even exist?
[Math] How many graphs is there, with 5 vertices and 3 edges of maximum degree 3
discrete mathematicsgraph theory
discrete mathematicsgraph theory
How many graphs is there, with 5 vertices and 3 edges of maximum degree 3?
I don't know if that graph even exist?
Best Answer
I will assume that the vertices are labeled.
There are $\dbinom{5}{2}=10$ possible edges. We want to pick three, so there are $\dbinom{10}{3}=120$ such graphs.
If the vertices aren't labeled, then there are only 4 configurations. Specifically, the edges can only assume the following configurations: /\ |, /|/, _|_, or a triangle.