Euler's formula for planar graphs Quiz

1. A connected planar graph has $v=6$ and $e=10$. How many faces does it have?

• A. $6$
• B. $4$
• C. $5$
• D. $14$

2. A connected planar graph has $10$ vertices and $7$ faces. How many edges does it have?

• A. $19$
• B. $15$
• C. $17$
• D. $5$

3. A tree has $6$ vertices. How many faces does it have?

• A. $0$
• B. $5$
• C. $1$
• D. $6$

4. An edge is added between two existing vertices of a connected planar graph without crossing any edge. What happens to the number of faces?

• A. It is unchanged
• B. It decreases by $1$
• C. It increases by $2$
• D. It increases by $1$

5. Which values $(v,\ e,\ f)$ could be a connected planar graph?

• A. $(6,\ 9,\ 6)$
• B. $(5,\ 7,\ 4)$
• C. $(4,\ 6,\ 3)$
• D. $(7,\ 10,\ 4)$