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Biconnectivity

# Biconnectivity - Biconnectivity 8:36 AM Outline and Reading...

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4/1/2003 8:36 AM Biconnectivity 1 Biconnectivity SEA PVD MIA SNA ORD FCO 4/1/2003 8:36 AM Biconnectivity 2 Outline and Reading Definitions Separation vertices and edges Biconnected graph Biconnected components Equivalence classes Linked edges and link components Algorithms Auxiliary graph Proxy graph 4/1/2003 8:36 AM Biconnectivity 3 Separation Edges and Vertices Definitions Let G be a connected graph A separation edge of G is an edge whose removal disconnects G A separation vertex of G is a vertex whose removal disconnects G Applications Separation edges and vertices represent single points of failure in a network and are critical to the operation of the network Example DFW, LGA and LAX are separation vertices (DFW,LAX) is a separation edge ORD PVD MIA DFW SFO LAX LGA HNL 4/1/2003 8:36 AM Biconnectivity 4 Biconnected Graph Equivalent definitions of a biconnected graph G Graph G has no separation edges and no separation vertices For any two vertices u and v of G , there are two disjoint simple paths between u and v (i.e., two simple paths between u and v that share no other vertices or edges) For any two vertices u and v of G , there is a simple cycle containing u and v Example ORD PVD MIA DFW SFO LAX LGA HNL 4/1/2003 8:36 AM Biconnectivity 5 Biconnected Components

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Biconnectivity - Biconnectivity 8:36 AM Outline and Reading...

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