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Unformatted text preview: 1 Â¡ 10 r n Â¡ 2 . Prove: if n 2 N , r n = 2 n +5 n . 6. Consider the graph G pictured to the right. (a) [3 pt] Find the chromatic number of G , Ã‚ ( G ). (b) [5 pt] Identify (i) an independent set that is not maximal, (ii) a maximal independent set; and (iii) compute the independence number of G , Â® ( G ). Clearly label each. (c) [2 pt] Yes or No: Are there any maximal independent sets in G that are not maximum? 7. TRUE or FALSE . Spell out the word you choose. (a) A connected graph must have a spanning tree. (b) Every tree with two or more vertices must have at least two leaves. (c) If f : A ! B is onetoone, and dom( f Â¡ 1 ) = B , then f is a bijection. (d) If the average degree of a connected graph is two, then the graph must be a tree. (e) There are 2 Â³ n 2 Â´ induced subgraphs of K n ....
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 Spring '10
 Jooe
 Graph Theory, Planar graph, complete graph, Symmetric graph

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