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In this chapter, we present some important concepts and algorithms from graph theory for the benefit of a general reader. These concepts and algorithms constitute the theoretical underpinnings of a variety of techniques used to solve the various problems that arise in the context of virtual craniofacial surgery. The focus of this chapter is to present the necessary graph-theoretic foundations for the research presented in the remainder of the monograph. The details of the graph-theoretic modeling of specific problems in the context of virtual craniofacial surgery, along with appropriate justifications, will be provided in later chapters. This chapter contains an introductory section, followed by three separate sections on graph matching, graph isomorphism, and network flow.
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