Question

A simple graph have 12 edges 5vertices of degree

Answer 1

Answer:

The two vertices aren't neighbours: (102)(85)2((82)2). Explanation: choosing the two, then neighbours for each, then a place for the two edges that's left.

The two vertices are neighbours: (102)(84)2((82)3)

In both cases there could be a third vertex with a degree 5 so we need to uncount it: (103)(73)3, choosing the 3 and then since they're all neighbours to each other, choose another 3 neighbors for each, which is exactly 12 edges.

The total is: (102)(85)2((82)2)+(102)(85)2((82)2)−(103)(73)3

hope it helps you friend ☺️