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Question

Suppose G be a connected planar graph of order n≥5 and size m. If the length of the smallest cycle in G is 5, then which of the following is true?

a.

(m+n)⁴>=mn

b.

m≤5/3(n−2)

c.

(m²+n)/3

d.

n>=(6/5)(n+1)

Answer: (b).m≤5/3(n−2)

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Q. Suppose G be a connected planar graph of order n≥5 and size m. If the length of the smallest cycle in G is 5, then which of the following is true?