Unformatted text preview: isomorphic , if there is a bijection f : X → X such that ( a,b ) ∈ R 1 i± ( f ( a ) ,f ( b )) ∈ R 2 . Count the binary relations of a 4-element set, if isomorphic relations are considered to be identical. (4) Let V be ²nite set. A graph on V is an irre³exive, symmetric relation on V . Count the graphs on a 5-elements set, if isomorphic graphs (de²ned by isomorphic relations) are considered to be identical. ( Hint: This is basically Exercise 54 of Chapter 14, and the method is outlined on pages 575–576. ) (5) Compute the number of non-equivalent colorings of the faces of a square pyramid with k colors. 1...
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- Fall '09
- Equivalence relation, Binary relation, Stained glass, Isomorphism