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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## This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec16_prob - Massachusetts Institute of...

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