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# notes123 - Notes Written by Michael Slate for the week of...

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Notes Written by Michael Slate for the week of April 15th - April 19th Monday April 15th, 2002 A graph G=(V, E) is: V - a set of vertices E - set of edges connecting vertices in V An edge E = (U, V) is a pair of vertices V = { A, B, C, D, E } E = { (A, B), (A, C), (B, C), (C, D), (D, E), (C, E) } Graphs can model real life problems like: Communication networks Electronic Circuits Transport Networks (i.e. streets, intersections, etc.) Event Dependencies Graph Terms Adjacent Vertices - vertices connected by an edge B, C, and D are adjacent to A Degree of Vertex - number of adjacent vertices (The degree of A is 3) Degree(V) = 2 * (number of edges) Path - sequence of Vertices, V1, V2, V3. ..Vk so that consecutive vertices Vi and V(i + 1 ) are adjacent.

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A, B, C, D is a path A, B, D is not a path Simple Path - a path with no repeated vertices Cycle - similar to a simple path except that the first vertext in path is same as last one. (i.e. A, B, C, A ) Connected Graph
Sub Graph - subset of vertices and edges of a graph Connected components - The maximal connected graphs of an original graph Tree - connected graph without a cycle Complete Graph - all pairs of vertices are adjacent o N is number vertices o M is number of edges o Example: M = N ( N - 1 ) / 2. Therefore, graph is not complete when M

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## This note was uploaded on 02/02/2012 for the course CS 251 taught by Professor Staff during the Fall '08 term at Purdue.

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notes123 - Notes Written by Michael Slate for the week of...

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