Discrete Mathematics with Graph Theory (3rd Edition) 280

Discrete Mathematics with Graph Theory (3rd Edition) 280 -...

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278 Solutions to Exercises 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 10. (a) Al = 0 0 1 0 1 0 1 0 A2 = 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 11. 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 (b) The function cp is an isomorphism because if the vertices of 91 are relabeled, Vi being replaced by CP(Vi) = Ui, then the adjacency matrix of 91 relative to the Ui'S is A 2. (See Theorem 10.3.3.) 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 (c) p = 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 (aJ [BB] P A ~ [ : q ~ 1 "A, but with row, written in the 0_ 2, 3, 1, the 0_ in which the y b rows of the 3 x 3 identity matrix were rearranged to give
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Unformatted text preview: P. (b) ApT = [~ ~ ; 1 is A, but with columns written in the order 2, 3, 1, the order in which the y z x rows of the 3 x 3 identity matrix were rearranged to give P. (cJ P APT ~ [t ~ : 1 i, A, hut with row, and columns written in the onI ... 2, 3, 1. 12 P A -[: t ~ ~ 1 is A, but with rows written in the order 3, 1,4,2, the order in which the . -; ~ ; ~ rows of the 4 x 4 identity matrix were written to make P. Ap T --[:z' :xa w: ~~ 1 I LA. U is A, but with columns written in the order 3, 1,4,2, the order in which the rows of the identity matrix were written to make P. P ApT = [~ : ; ~ 1 is A, but with rows and columns written i the order 3, 1,4,2. r p s q 13. (a) [BB] The matrices are the adjacency matrices of graphs 91, 92, respectively. Since 92 has three...
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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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