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MIT6_042JS10_lec17

# MIT6_042JS10_lec17 - Connected Components Mathematics for...

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1 Albert R Meyer, March 12, 2010 Graph Connectivity Trees lec 6F.1 Mathematics for Computer Science MIT 6.042J/18.062J Albert R Meyer, March 12, 2010 Connected Components Every graph consists of separate connected pieces (subgraphs) called connected components lec 6F.2 Albert R Meyer, March 12, 2010 Connected Components East Campus E25 Med Center E17 4 Infinite corridor 13 10 12 26 8 16 66 3 connected components the more connected components, the more “broken up" the graph is. lec 6F.3 Albert R Meyer, March 12, 2010 Connected Components The connected component of vertex v ::= lec 6F.4 Albert R Meyer, March 12, 2010 Connected Components So a graph is connected iff it has only 1 connected component lec 6F.5 Albert R Meyer, March 12, 2010 Def: vertices v , w are k-edge connected if they remain connected whenever fewer than k edges are deleted. lec 6F.6 Edge Connectedness

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2 Albert R Meyer, March 12, 2010 k-edge Connectedness lec 6F.8 1- edge connected no path Albert R Meyer, March 12, 2010 Edge Connectedness lec 6F.9 2- edge connected no path
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MIT6_042JS10_lec17 - Connected Components Mathematics for...

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