Transcription of 5 Graph Theory - MIT OpenCourseWare
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5 Graph Theory - MIT OpenCourseWare
Mcs-ftl 2010/9/8 0:40 page 121 #1275 Graph TheoryInformally, a Graph is a bunch of dots and lines where the lines connect some pairsof dots. An example is shown in The dots are callednodes(orvertices)and the lines are example of a Graph with 9 nodes and 8 are ubiquitous in computer science because they provide a handy wayto represent a relationship between pairs of objects. The objects represent itemsof interest such as programs, people, cities, or web pages, and we place an edgebetween a pair of nodes if they are related in a certain way. For example, an edgebetween a pair of people might indicate that they like (or, in alternate scenarios,that they don t like) each other. An edge between a pair of courses might indicatethat one needs to be taken before the this chapter, we will focus our attention on simple graphs where the relation-ship denoted by an edge is symmetric. Afterward, in Chapter6, we consider thesituation where the edge denotes a one-way relationship , for example, where oneweb page points to the Simple GraphsDefinition graphGconsists of a nonempty setV, called thever-tices(akanodes2) ofG, and a setEof two-element subsets ofV.
situation where the edge denotes a one-way relationship, for example, where one web page points to the other.1 5.1 Definitions 5.1.1 Simple Graphs Definition 5.1.1. A simple graph Gconsists of a nonempty set V, called the ver-tices (aka nodes2) of G, and a set Eof two-element subsets of V. The members
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