ECE 320 Networks and Systems
Spring 2007–2008
Problem Set 6
Not due.
1. You are concerned with communication networks for sensors. You describe the system as a graph where
the vertices are the sensors and the edges are the communication links. The communication links are
unidirectional, so the graph is a directed graph. A sensor does not talk to itself via a communication
link so the graph has no self loops. Because the network is composed of sensors, you are more concerned
with communication of information from a sensor rather than to a sensor. Because you are concerned
with the failure of communication links, you would like each sensor to have two links leading away
from the sensor. Because you are concerned with cost, you would like each sensor to have exactly two
links leading away from the sensor.
(a) For the case of
n
= 9 sensors, please draw the graph that is the worst possible case in the sense
of the maximum number of components given that each vertex has two edges leaving that vertex.
This is clearly a very poor arrangement for a network.
(b) For the case of
n
= 9 sensors, please draw a graph in which each vertex has two edges leaving
that vertex and the removal of any edge leaves the graph strongly connected.
This is at least a
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 Spring '06
 FINE
 Probability theory, Randomness, Monte Carlo method, communication networks, communication links

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