notes123

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online