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ams301-1hw - AMS 301.1 HOMEWORK 1 Prof Tucker Spring 2008...

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AMS 301.1 HOMEWORK # 1 Prof. Tucker Spring, 2008 Section 1.1: for 1,9,23-- see answer in back of text; 6a) 5 vertices, b) 9 vertices; 14.,many possibilities, 16a) ( a , b ), ( a , g ) and ( c , d ), ( d , e) and ( c,d ), ( e , f) and ( d , e ), ( e , f ), b) { b ,g } , { b ,f } , { c , f }, { c , e }, { d , f }, c) 3 (the edges incident to any vertex); 20. . O O O O O O O O Block surveillance vertices = • Corner surveillance vertices = a) b) O O O c) O O O O Section 1.2 : 5bck 7, see answer in back: 4. Not isomorphic , 6c) no, complement of left graph is 2 4-circuits, d) no, 5-degree and degree-3 vertices form a triangle only in right graph, e) No, only right graph has triangles; Section 1.3 : 1, See answer in back of text: 4. n is odd and so parity of deg. is samein complement. Ans: n -1 6. Make graph with vertex = team, edge = game. Within a given conference, the subgraph consists of 13 vertices, each of degree 11— contradicting Corollary 10b) (A,Z)- (B,X)-(C,Y) - (D,W) - (C,U) - (B,V) - (A,T) - (B,R)- (C,S) - (M,M) .
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