Discrete Mathematics with Graph Theory (3rd Edition) 265

Discrete Mathematics with Graph Theory (3rd Edition) 265 -...

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Section 10.1 17. (a) Not isomorphic: IC4 has four vertices while IC 3 ,8 has 11. (b) Not isomorphic: IC n has CD = 55 edges while IC 3 ,8 has 24. (c) Not isomorphic: IC 4,6 has ten vertices while IC2,12 has 14. (d) Not isomorphic: IC 4,6 has 24 edges while IC 5 ,5 has 25. 263 (e) Isomorphic: in fact, these are the same graph simply viewed in different ways. In each case, the graph consists of a set of four vertices each of which is joined in all possible ways to the vertices in a second set of six. 18. No. Let (h and fh be any pair of graphs which are not isomorphic and set 93 = 91. The conditions hold but 91 ~ 93' 19. In this case, George's deduction is correct. To see why most easily, recall that the notion of "isomor- phism" is an equivalence relation. Thus, if 91 is not isomorphic to 92, then 91 and 92 are in different equivalence classes. If (h ~ 93, then 92 and 93 are in the same equivalence class. Thus 91 and 93 are in different equivalence classes and hence not isomorphic.
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