Discrete Mathematics with Graph Theory (3rd Edition) 259

Discrete Mathematics with Graph Theory (3rd Edition) 259 -...

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Section 9.3 3. (a) [BB] 0 o (b) o o o 0 0,0,0 G---E> 1,1,0 o 0 0 G---E) o G---E) G---E) 2,1,1 2,2,2 0,0,0,0 1,1,0,0 1,1,1,1 2,1,1,0 2,2,2,0 2,2,1,1 3,1,1,1 3,2,2,1 2,2,2,2 3,3,2,2 3,3,3,3 257 4. (a) These graphs are not isomorphic. Vertex q has degree 4 but the other graph has no vertex of degree 4. (b) [BB] These graphs are isomorphic. One possible isomorphism is given by as illustrated. cp(A) = p, cp(B) = t, cp(C) = u, cp(D) = v, cp(E) = Q, cp(F) = s, cp(G)
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Unformatted text preview: = r A XX r C DF G vD (c) These graphs are not isomorphic. Consider the unique vertices B and r of degree 3 in each graph. Vertex B is adjacent to two vertices of degree 1, but vertex r is not. (d) These graphs are isomorphic. One possible isomorphism is given by as illustrated. cp(A) = p, cp(B) = q, cp(C) = u, cp(D) = t, cp(E) = w, cp(F) = r, cp(G) = v, cp(H) = s A D 1M1 B C BWi PA D q C t u w v r s F H 5. (a) [BB] No; it has a vertex of degree 5....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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