Question

Which one of the following represents the total number of faces in the given graph

• A. \(4\)
• B. \(7\)
• C. \(8\)
• D. \(6\)

Hint:

Use Euler’s formula: \(F = E - V + 2\).

Answer 1

The Correct Option is C

Step 1: Recall Euler formula for planar graphs.
For any connected planar graph, Euler formula states $V - E + F = 2$, which rearranges to $F = E - V + 2$, where $V$ = vertices, $E$ = edges, and $F$ = faces (including the unbounded outer face).

Step 2: Read the graph parameters.
From the given graph: vertices $V = 5$ and edges $E = 11$.

Step 3: Calculate the number of faces.
$F = E - V + 2 = 11 - 5 + 2 = 8$. This includes 7 interior bounded faces and 1 exterior unbounded face. \[ \boxed{8} \]