Transcription of Graph Theory
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Graph Theory
1 Graph Theory Begin at the beginning, the King said, gravely, and go on till youcome to the end; then stop. Lewis Carroll,Alice in WonderlandThe Pregolya River passes through a city once known as K onigsberg. In the 1700sseven bridges were situated across this river in a manner similar to what you seein Figure The city s residents enjoyed strolling on these bridges, but, as hardas they tried, no resident of the city was ever able to walk a route that crossed eachof these bridges exactly once. The Swiss mathematician Leonhard Euler learnedof this frustrating phenomenon, and in 1736 he wrote an article [98] about work on the K onigsberg Bridge Problem is considered by many to be thebeginning of the field of Graph The bridges in K Harris et al.
6 1. Graph Theory The closed neighborhood of a vertex v, denoted by N[v], is simply the set {v} ∪ N(v). Given a set S of vertices, we define the neighborhood of S, denoted by N(S), to be the union of the neighborhoods of the vertices in S.
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