Question 4 Cayley Graphs. For parts (b-c), let G be a group and x = G. (a) Draw the Cayley graph of Z8 over 3 (operation is +). (b) Using properties of groups, explain why the following cannot be a subgraph of the Cayley graph of G over x x V1 u x V2 (c) Suppose y Є G and y x. Draw enough of the Cayley graph of G over {x,y} to convince me that (xy)-1=y-¹×¹

Question 4 Cayley Graphs. For parts (b-c), let G be a group and x = G. (a) Draw the Cayley graph of Z8 over 3 (operation is +). (b) Using properties of groups, explain why the following cannot be a subgraph of the Cayley graph of G over x x V1 u x V2 (c) Suppose y Є G and y x. Draw enough of the Cayley graph of G over {x,y} to convince me that (xy)-1=y-¹×¹

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 45E: 45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )

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