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Unformatted text preview: T ( x ) = x (1 + x + 2 x 2 + 5 x 3 ) 1xx 22 x 35 x 4 . 5. (5 points) Up to isomorphism, how many 3regular 8vertex graphs are there that have no cycle of length 3? (Justify your answer.) 6. (6 points) For n N 1 , let G n = ( V n ,E n ) be the graph where V n = { 1 , 2 ,...,n } { 1 , 2 ,...,n } and two distict vertices ( a 1 ,b 1 ) and ( a 2 ,b 2 ) are adjacent if and only if either a 1 = a 2 or b 1 = b 2 . i Draw G 3 . ii Show that G 3 is isomorphic to its complement. (The complement of a graph G = ( V,E ) is the graph G c = ( V,E c ) where each pair of vertices is adjacent in G c if and only if they age not adjacent in G .) iii Is G 4 isomorphic to its complement? (Why?)...
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 Spring '09
 M.PEI
 Math

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