It is Graphic theory problem thanks for the help Please Let

It is Graphic theory problem, thanks for the help

Please, Let G be a connected cubic simple graph that contains 2 spanning trees with no edges in common, show that |G|=4

Solution

Let G be a simple cubic graph, with two edge-disjoint spanning trees, that has n vertices and m edges. Since G is regular of degree 3, we have

3n=2m.

Now any spanning tree has n1 edges, and G has two disjoint spanning trees. So we have

m2n2.

Combining the first equation and the second inequality, we get

n4.

Now there are no cubic simple graphs on 1, 2 or 3 vertices.