Date of Award

Spring 2004

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Mathematics, Statistics and Computer Science

First Advisor

Factor, Kim

Second Advisor

Factor, James

Third Advisor

Struble, Craig

Abstract

In today's fast paced world, the nature of information being exchanged over networks is becoming increasingly multifaceted. This has created the need for different types of reliable networks. This research is a theory based investigation aimed at analyzing different communication network structures using graph theory. In our study, we assume that each network has a communication center responsible for transmitting information to and receiving information from all the other nodes of the network. We call this communication center the principal node of the network. This research focuses on the problem of determining the principal node of a network, based on the availability of standby nodes. Networks are modeled using tournaments: a graph where every pair of vertices is connected by a single uniquely directed edge that represents the direction of flow of information. A new approach, using domination graph theory, is presented to determine the availability of standby nodes. Based on the availability of standby nodes, a node is selected as the communication center in the network.

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