Graph Theory: 58. Euler's Formula for Plane Graphs

In a connected plane graph with n vertices, m edges and r regions, Euler's Formula says that n-m+r=2. In this video we try out a few examples and then prove this fact by induction. We discuss a generalization to disconnected plane graphs as well as what Euler's Formula means for a polyhedron.
-- Bits of Graph Theory by Dr. Sarada Herke.


Related videos:
GT 57 Planar Graphs -    • Graph Theory: 57. Planar Graphs  
GT 55 Bridges and Blocks -    • Graph Theory: 55. Bridges and Blocks  

For the proof that in a tree on n vertices, the number of edges is n-1, check out this video:
GT 37: Which Graphs are Trees -    • Graph Theory 37. Which Graphs are Trees  

For the proof that an edge is a bridge if and only if it lies on no cycle, check out this video:
GT 34: Bridge edges -    • Graph Theory: 34. Bridge edges  

For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" -    / spoonfulofmaths  



Video Production by: Giuseppe Geracitano (goo.gl/O8TURb)