Hi,

I have an exercise about graphs which I cannot solve. Could you please help me?

The exercise is as follows:

Thank you very muchA simple graph, also called a strict graph, is an unweighted, undirected graph containing no graph loops or multiple edges. A well-known theorem states that the sum of the degrees of the vertices of a simple graph equals twice the number of edges of the graph.

Prove the following:

There is no simple graph with 12 vertices and 28 edges so that

(i) all vertices have degree 3 or 4

(ii) all vertices have degree 3 or 6