Recall the definition of graph isomorphism from Exercise 47.21. We call a graph G self-complementary if G is isomorphic to G. a. Show that the graph G D fa; b; c; dg; fab; bc; cdg is self-complementary. b. Find a self-complementary graph with five vertices. c. Prove that if a self-complementary graph has n vertices, then n 0 .mod 4/ or n 1 .mod 4/.

Lecture 1: Introduction Simplify the Expressions: 1. 5(3x+4)-4 = 15x+20-4 = 15x+16 2. 4(5y-3)-(6y+3) = 20y-12-6y-3 = 24y-15 3. l -5-3 l = l-8 l = 8 Order of Operations Please Excuse My Dear Aunt Sally = Parenthesis Exponents Multiplication Division Addition Subtraction Exponents: 3 2 5 1. (x 1/3x 2/3 x 1 2. (x ) (x ) = x =x 3. (x ) = x 12 4. y / y = y 3 0 5. z =-2 2 6. ¼ = 4 = 16 7. 1/(-x) = (-x)2 8. 7x y = 7y /x 5 9. (-3x y ) = 81x y 12 Square Roots: 1. √81 = 9 2 2. √81x = 9x 3. √100/9 = 10/3 4. √500 = √5(100) = 10 √5 5. √ 48 x /√6 x = √8x 2 = 2x √2 6. 5 √x+7 x√12√ x 7√ √ 12=7 3+√ 3=9√√ 7. 8. 1/ √ 7= √/7