# ch7 - Graphs and Graph Traversals Section 7.1 Graphs can...

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Graphs and Graph Traversals Section 7.1 Graphs can solve several problems in linear time -- easy problems. Graphs of million nodes can be solved. Other problems require revisiting nodes of the graph – medium problems. Polynomial time problems such as n 2 , n 3 . Graphs with thousands or tens of thousands can be solved. Still other problems are hard, requiring revisiting nodes of the graph several times. 2 n . Graphs with 50 to 100 nodes can be solved. Section 7.2 Definitions and Representations Graph is a 2 tuple G = (V,E) set of Vertices or nodes - V set of Edges: E V x V undirected are two way directed are one way Examples: airline routes, flowcharts, binary relation, computer networks, electrical circuits subgraph some of a graph – given G=(V,E), G’=(V’,E’) where V’ V, E’ E. G’ is a subgraph of G. symmetric digraph - if there exists an edge uv there must be an edge vu. adjacency relation - two vertices connected by an edge.

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ch7 - Graphs and Graph Traversals Section 7.1 Graphs can...

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