S08.hw06 - ECE 320 Networks and Systems Spring 20072008...

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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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