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.
The vertex set of a graph G is denoted by V(G), and the edge set is denoted by E(G). We may refer to these sets simply as V and E if the context makes the particular graph clear. For notational convenience,instead of representingan edge as {u,v }, we denote this simply by uv . The order of a graph G is the cardinality
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