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Unformatted text preview: nsubsets of the set { 1 , 2 ,..., 2 n +1 } , and where two vertices are adjacent if and only if they are disjoint. (a) Show that O (2) is isomorphic to the Petersen graph depicted in Figure 1. (b) Prove that O ( n ) is connected. Figure 1: The Petersen graph 4. Let G be a graph with at least two vertices, such that the cut induced by every proper nonempty subset of vertices of G contains exactly two elements. Determine (with proof) the number of vertices and edges in G . 1...
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 Fall '09
 M.PEI
 Math, Combinatorics

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