A simple graph is called self-complementary if it is isomorphic to its complement. Let G be a self-complementary graph.

1 v v 4 [a] Prove that the erder of G must be either 4!; er 4!: + 1 for seme nonnegative integer k. (Hint: what must |E[G]| equal?) (13) If {(11, d2, . . . (in) is the degree sequence of G then what is i. 2;; d5, and ii. d.- + dn+1_1- fer eaeh i E nf2? iii. Can d1 = e? [c] Find all selfeemplementarj,r graphs of degree 4 (up to isomorphism). [d] Find all selfeemplementsry graphs ef degree 5 (up to isomorphism). (Hint: rst deter mine which degree sequenees are possible.)