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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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 Fall '08
 EGGEN,R
 Algorithms

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