# hw5 - Problem C Read Section 9.4 Let G and H be simple...

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MATH 145: HOMEWORK 4 ANDREW BERGET This is due Friday February 19. Problem A. Is there a simple graph on 5 vertices { v 1 , v 2 , v 3 , v 4 , v 5 } with deg( v i ) = i . Do not do this by attempting to draw every graph on 5 vertices. Problem B. The complement of a simple graph G = ( V ( G ) , E ( G )) is the the graph ¯ G with the same vertex set V ( G ) and edge set {{ u, v } : { u, v } / E ( G ) } . Given an example of a graph G such that G is connected but ¯ G is not. Give an example of a graph H such that H is disconnected but ¯ H is not. (This is false! Try to prove it.)
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Unformatted text preview: Problem C. Read Section 9.4. Let G and H be simple graphs. Prove that G and H are isomorphic graphs if and only if ¯ G and ¯ H are isomorphic graphs. Problem D. Solve Problem 9.2. Then either prove or disprove the statement: In an Eulerian graph (i.e., a graph containing an Eulerian circuit) with an even number of vertices, the number of edges is even. Solve Problems 9.23, 9.27, 9.29, 9.38, 9.39+. 1...
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