Question
Let `delta` denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices
with `delta` `ge` 3, which one of the following is TRUE?
Answer: Option A
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We know that v + r = e + 2 `rArr` e = n + r - 2 ... (1)
Where V = n(number of vertices) ;r number of faces and
e = number of edges
Given, `delta` `ge` 3 then 3n `ge` 2e
`rArr` e `ge` `(3n)/2`
`rArr` n + r - 2 `ge` `(3n)/2` (u sin g (1))
`rArr` r `ge` `(3n)/2` - n + 2 `rArr` r `ge` `n/2` + 2
`:.` Number of faces is atleast `n/2` + 2
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