I'm doing university exercises about planar graphs and they gave me the following:
Let G be a connected, self-complementary planar graph of order n and size m having four vertices of degree two and the remaining vertices of degree d. If six faces of G are triangles and the remaining faces are pentagons, compute the values of d, n and m.
I'm not sure How Can I figure out the solicited values? I tried reach an equalization using the Euler form, the successions degree form and the sizes form for a complementary graph, but I had not success.
Has someone any idea ?
Thanks a lot!