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Unformatted text preview: Graphs Discrete Math MATH 135 David Oury Graphs Discrete Math MATH 135 David Oury August 23, 2011 Chapter 9 of Discrete Mathematics and its Applications, by Rosen Graphs Discrete Math MATH 135 David Oury Graphs I Definition: graph A graph G has two parts A set V of vertices . A collection E of edges . An edge is a pair of vertices. Duplicate pairs are allowed in the collection of edges. In a (undirected) graph each edge is a unordered pair vertices. In a directed graph each edge is an ordered pair of vertices. In a simple graph no duplicate edges/pairs exist and every edge has distinct endpoints. Graphs Discrete Math MATH 135 David Oury Graphs II Example: flight paths An airline has scheduled flights between a certain set of cities. The set of cities are the vertices of a graph. There is an edge between a pair of cities if the airline has scheduled flights between those two cities. We have a simple (undirected) graph. Definition: subgraph, proper subgraph A subgraph of a graph G = ( V , E ) is a graph G = ( V , E ) with V V and E E where the endpoints of E are in V . A proper subgraph has either V ( V or E ( E (so G 6 = G .) Graphs Discrete Math MATH 135 David Oury Graphs III Definition: union of graphs The union G = ( V , E ) of simple graphs...
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