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TERMINOLOGY AND BASIC GRAPH THEORY
Introduction
This chapter presents an overview of basic graph theory, including its association with set
theory. Graphs can be shown to be quite useful, especially as a mathematical tool for
studying network problems. We shall begin our study with graph theory as applied to
static problems in network theory, which are those problems that are related to the
structure of the network. Static problems include the assessment of the impact of the loss
of one or more communicating nodes or one or more communication links. We use
graph theory in an attempt to create networks that are less vulnerable to such loss.
In another chapter of these notes, we shall consider the application of graph theory to
dynamic problems, such as dynamic load balancing. We shall show that certain
algorithms become unstable under dynamic conditions, in that they present alternating
optimal solutions: try this, no try that, etc. This observation should serve as a caution not
to...

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