Math Help - graph theory

1. graph theory

1)determine |v|,given that G=(v,e) is regular graph with 12 edges?2)let G=(V,E) be a connected graph.What is the largest possible value of|V| if |E|=16 and deg(v)>=5 for all v belonging V?

2. Re: graph theory

Originally Posted by panelopy123
1)determine |v|,given that G=(v,e) is regular graph with 12 edges?2)let G=(V,E) be a connected graph.What is the largest possible value of|V| if |E|=16 and deg(v)>=5 for all v belonging V?

You failed to say if these questions are about simple graphs or not.

Lets assume they are. You should know that $\sum\limits_{v \in V} {\deg (v)} = 2\left| E \right|$.
Then what is a regular graph? If you know that the answer to the first is immediate.

The complete graph $\mathcal{K}_6$ has each vertex of degree five.
However, $|E|=15$ and $\ne16$. If these are not simple graphs then we can add an edge,

3. Re: graph theory

its a simple graph.