Slide09 Graphs

# Slide09 Graphs - D iscrete Mathematics Discrete...

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Discrete Mathematics Discrete Mathematics (2009 Spring) Graphs (Chapter 9, 5 hours) Chih-Wei Yi Dept. of Computer Science National Chiao Tung University June 1, 2009

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Discrete Mathematics Chapter 9 Graphs §9.1 Graphs and Graph Models What are Graphs? General meaning in everyday math: A plot or chart of numerical data using a coordinate system. Not Technical meaning in discrete mathematics: A particular class of discrete structures (to be de°ned) that is useful for representing relations and has a convenient webby-looking graphical representation.
Discrete Mathematics Chapter 9 Graphs §9.1 Graphs and Graph Models Simple Graphs Correspond to symmetric binary relations R . Visual Representation of a Simple Graph A simple graph G = ( V , E ) consists of: 1 A set V of vertices or nodes ( V corresponds to the universe of the relation R ). 2 A set E of edges / arcs / links: unordered pairs of [distinct?] elements u , v 2 V , such that uRv .

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Discrete Mathematics Chapter 9 Graphs §9.1 Graphs and Graph Models Example of a Simple Graph Let V be the set of states in the far-southeastern U.S.: V = f FL,GA,AL,MS,LA,SC,TN,NC g . Let E = ff u , v g j u adjoins = 8 < : {FL,GA},{FL,AL},{FL,MS},{FL,LA},{GA,AL}, {AL,MS},{MS,LA},{GA,SC},{GA,TN},{SC,NC}, {NC,TN},{MS,TN},{MS,AL} 9 = ; . TN AL MS LA SC GA FL NC