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# lec0422-Graphs - Announcements MP 7 available EC Due 4/22...

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Announcements: MP 7 available. EC Due 4/22, 11:59p. Due 5/2, 11:59p. Today: Graphs - Weiss, Chapter 9

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How do we get from here to there? Need: 1. Common Vocabulary 2. Graph implementation 3. Traversal 4. Algorithms.
Graph Vocabulary: Incident edges(6) Degree(6) Adjacent vertices(6) Path(G 2 ) Cycle(G 1 ) Simple graph(G) G = (V,E) |V| = n |E| = m G 1 G 2 G 3

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Graph Vocabulary: Subgraph(G) – G’ = (V’, E’), V’__ V, E’ ___ E, and (u,v) ___ E’ implies u___V’ and v ___ V’. Complete subgraph(G 2 ) – Connected component(G) – Acyclic subgraph(G 2 ) – Spanning tree(G 1 ) – G = (V,E) |V| = n |E| = m G 1 G 2 G 3
Graphs: theory that will help us in analysis How many edges? At least: connected – not connected - At most: simple - not simple - Relationship to degree sum: X U V W Z Y a c b e d f g h deg( v ) = v V G = (V,E) |V| = n |E| = m Running times often reported in terms of n, the number of vertices, but they often depend on m, the number of edges.

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Thm: Every minimally connected graph G=(V,E) has |V|-1 edges.
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