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Unformatted text preview: x, 0). If ( x,y ) = (0 , 4), then the equation ( xy )( p + q ) = ( pq )( x + y ) reduces to 0( p + q ) = ( pq )4. So this means either p or q must also be zero and, then, it doesn’t matter what value we give to the other. 3. Graph isomorphism (a) Prove that the following two graphs are isomorphic. That is, for each vertex in G 1, give the corresponding vertex in G 2, making sure your mapping preserves the edge structure. G1: A B C D E G2: 1 5 3 4 2 Solution: A corresponds to 1, B corresponds to 5, C corresponds to 3, D corre-sponds to 4, and E corresponds to 2. (b) Prove that the following two graphs are not isomorphic. 2 G1: A B C D E G2: 1 2 3 4 5 Solution: They can’t be isomorphic because vertex 1 in G 2 has degree 4, but none of the vertices in G 1 has degree 4. 3...
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- Spring '11
- Equivalence relation, Binary relation, equivalence classes, Isomorphism