MIT6_042JS10_lec16_prob

MIT6_042JS10_lec16_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science March 10 Prof. Albert R. Meyer revised March 2, 2010, 734 minutes In-Class Problems Week 6, Wed. Problem 1. For each of the following pairs of graphs, either define an isomorphism between them, or prove that there is none. (We write ab as shorthand for a b .) (a) G 1 with V 1 = { 1 , 2 , 3 , 4 , 5 , 6 } , E 1 = { 12 , 23 , 34 , 14 , 15 , 35 , 45 } G 2 with V 2 = { 1 , 2 , 3 , 4 , 5 , 6 } , E 2 = { 12 , 23 , 34 , 45 , 51 , 24 , 25 } (b) G 3 with V 3 = { 1 , 2 , 3 , 4 , 5 , 6 } , E 3 = { 12 , 23 , 34 , 14 , 45 , 56 , 26 } G 4 with V 4 = { a,b,c,d,e,f } , E 4 = { ab,bc,cd,de,ae,ef,cf } (c) G 5 with V 5 = { a,b,c,d,e,f,g,h } , E 5 = { ab,bc,cd,ad,ef,fg,gh,he,dh,bf } G 6 with V 6 = { s,t,u,v,w,x,y,z } , E 6 = { st,tu,uv,sv,wx,xy,yz,wz,sw,vz } Problem 2. Definition 10.2.5 . A graph is connected iff there is a path between every pair of its vertices. False
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MIT6_042JS10_lec16_prob - Massachusetts Institute of...

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