离散数学及其应用英文版第五版

SECTION 8.2

Q4:

( Q4 )

34 a)Assume that 2e/v < m.Let G=(V ,E) be the graph with v vertices and e edges.

∵ m is the minimum degree of the vertices of G

∴

v' V

( Q4在三维空间中投影 的另一种视觉效果) deg(v') m*v

deg(v') > 2e

v' V ∵2e/v < m ∴2e <m*v ∴v' V But from the handshaking theorem,we know that deg(v') = 2e

∴2e/v m

b). Assume that 2e/v > M.Let G=(V ,E) be the graph with v vertices and e edges.

∵ M is the maximum degree of the vertices of G

∴

v' V deg(v') M*v

deg(v') < 2e

v' V ∵2e/v > M ∴2e >M*v ∴v' V But from the handshaking theorem,we know that

∴2e/v M

SECTION 8.3 deg(v') = 2e

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