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.


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GT 57 Planar Graphs - [ Ссылка ]
GT 55 Bridges and Blocks - [ Ссылка ]

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 - [ Ссылка ]

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 - [ Ссылка ]

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



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

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