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MIT6_042JS10_lec11

# MIT6_042JS10_lec11 - Mathematics for Computer Science MIT...

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1 Albert R Meyer, March 1, 2010 Mathematics for Computer Science MIT 6.042J/18.062J Directed Graphs lec 5M.1 Albert R Meyer, March 1, 2010 lec 5M.2 Digraphs a set, V , of vertices a set, E V × V of directed edges (v,w) E v w notation: v w Albert R Meyer, March 1, 2010 Relations and Graphs a c b d V = { a , b , c , d } E = {( a,b ), ( a,c ), ( c,b )} lec 5M.3 Albert R Meyer, March 1, 2010 Formally, a digraph with vertices V is the same as a binary relation on V . lec 5M.4 Digraphs

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2 Albert R Meyer, March 1, 2010 Graphical Properties of Relations Reflexive Transitive Symmetric Asymmetric NO lec 5M.6 Albert R Meyer, March 1, 2010 Graph of Strict Partial Order a b c e d f lec 5M.15 Albert R Meyer, March 1, 2010 how to check? no self-loops i i E ( irreflexive ) if edges i j and j k then shortcut edge i k is there too ( transitive ) Graph of Strict Partial Order lec 5M.16 Albert R Meyer, March 1, 2010 Cycles A cycle is a positive length directed path that starts and ends at the same vertex.
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MIT6_042JS10_lec11 - Mathematics for Computer Science MIT...

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