2. Application

A wired network is a non-empty set of computers and ethernet connections.

Each ethernet connection is between exactly two computers in the network. If there

is an ethernet connection between computers C and D, then we can say that C

connects to D and D connects to C.

A pair of computers can have at most one ethernet connection between them.

A data line between distinct computers C, D is a sequence of connections that

starts at C and concludes at D. For example, C, D could have the sequence

((C, C₁), (C₁, C₂),..., (Cn, D)) where C connects to C₁, then C₁ connects to C2,

and so on to C₁ which finally connects to D.

A wired network where every pair of computers has a data line between them is

called a connected wired network.

Assume computers can be constructed with any number of ethernet ports to sup-

port being participants in any number of ethernet connections.

(a) Draw three different connected wired networks for the computers C₁, C2, C3.

(b) Prove or Disprove: In any connected wired network, there are more

computers than ethernet connections.