Euler's formula for planar graphsAQA A-Level Further Maths: Mind map

Exam questions on Euler's formula for planar graphs

1. A connected planar graph $G$ has $8$ vertices and $12$ edges.
   Every face of $G$, including the outer face, is bounded by the same number of edges. Find this number.2 marks
2. A connected simple planar graph has $7$ vertices, and every face, including the outer face, is bounded by exactly $3$ edges.
   Find the number of faces, and state how many of them are bounded faces, not counting the outer face.2 marks
3. A connected planar graph has $9$ vertices, and its edges divide the plane into $8$ faces, including the outer face.
   Find the number of edges.3 marks