MIT6_042JF10_rec06_sol - 6.042/18.062J Mathematics for...

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Unformatted text preview: 6.042/18.062J Mathematics for Computer Science September 29, 2010 Tom Leighton and Marten van Dijk Notes for Recitation 6 1 Graph Basics Let G = ( V,E ) be a graph. Here is a picture of a graph. A B C D F E G Recall that the elements of V are called vertices, and those of E are called edges. In this example the vertices are { A,B,C,D,E,F,G } and the edges are { A — B,B — D,C — D,A — C,E — F,C — E,E — G } . Deleting some vertices or edges from a graph leaves a subgraph . Formally, a subgraph of G = ( V,E ) is a graph G = ( V ,E ) where V is a nonempty subset of V and E is a subset of E . Since a subgraph is itself a graph, the endpoints of every edge in E must be vertices in V . For example, V = { A,B,C,D } and E = { A — B,B — D,C — D,A — C } forms a subgraph of G . In the special case where we only remove edges incident to removed nodes, we say that G is the subgraph induced on V if E = { ( x — y | x,y ∈ V and x — y ∈ E } . In other words, we keep all edges...
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This note was uploaded on 01/19/2012 for the course CS 6.042J / 1 taught by Professor Tomleighton,dr.martenvandijk during the Fall '10 term at MIT.

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MIT6_042JF10_rec06_sol - 6.042/18.062J Mathematics for...

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