Euler Formula Examples

Graph Theory · Axiom Academy

EXAMPLE Euler's Formula Examples Applying V - E + F = 2 to analyze planar graphs Excellent work! You've mastered Euler's formula for planar graphs. Here's what we learned: Euler's Formula: For any connected planar graph, V - E + F = 2, where V is vertices, E is edges, and F is faces (including the outer infinite face). Systematic Counting: When counting faces, always remember to include the outer/exterior face that surrounds the entire graph. Finding Unknown Values: If you know any two of V, E, or F, you can use Euler's formula to find the third: V = E - F + 2, E = V + F - 2, or F = E - V + 2. Edge Bounds: For simple planar graphs with V ≥ 3, we have E ≤ 3V - 6. This bound helps us determine if a graph can be planar. Verification Tool: Euler's formula serves as a quick check for whether your counting is correct - if V - E + F ≠ 2, you made a counting error! These techniques are fundamental in graph theory. Use Euler's formula to analyze connectivity, planarity, and structural properties of graphs!

This is the written version of the interactive lesson above. See the full Graph Theory course.