I'm doing a question in my text that asks me to find how many regions a graph has if it has 6 vertices all of which has degree 4. I know i'm supposed to use the euler theorem of $r=e-v+2$, but to use this I need to find the number of edges first. So how do I find the number of edges in a graph if I know how many vertices there are and their degrees?
[Math] Finding number of edges given vertices and degree sequence
graph theory
Best Answer
The sum of the vertex degree values is twice the number of edges, because each of the edges has been counted from both ends.
In your case $6$ vertices of degree $4$ mean there are $(6\times 4) / 2 = 12$ edges.