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9.3: Representing Graphs and Graph Isomorphism

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Graphs, Edge tables, and adjacency matrices a bababab cdcdcdc edge lists Vertex adjacency vertexinitial vertex terminal vertex adjacency matrices

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1-1 correspondence Def: When 2 simple graphs G1=(V1,E1) and G2=(V2,E2), there is a one-to-one correspondence (one-to-one and onto) between vertices of the two graphs that preserves the adjacency relationship. (i.e.: a and b are adjacent in G1 iff f(a) and f(b) are adjacent in G2). Examples:

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Examples (sketch03)

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How can you tell if 2 graphs are isomorphic, or not? It can be hard to tell, and it is impractical to check all n! possible correspondences. Two graphs are not isomorphic if they do not share an invariant property Question: Name some properties that two isomorphic graphs should share. Examples:

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More examples B A C AC E DED # vertices# edgesDegreesCorresponding vertices Corresponding subgroups

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More examples # vertices# edgesDegreesCorresponding vertices Corresponding subgroups

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Define a 1-1 correspondence between vertices Example

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Section 2.1 Notes: Relations and Functions

Section 2.1 Notes: Relations and Functions

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