14. Solve the following:(a) If graph G is self-complementary (see Problem 1):(i) Determine |E| if |V | = n.(ii) Prove that G is connected.(b) Let n = 4k or n = 4k + 1 for a non-negative number k. Prove that there exists a self-complementary graph G = (V, E) where |V | = n.

14. Solve the following:(a) If graph G is self-complementary (see Problem 1):(i) Determine |E| if |V | = n.(ii) Prove that G is connected.(b) Let n = 4k or n = 4k + 1 for a non-negative number k. Prove that there exists a self-complementary graph G = (V, E) where |V | = n.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.3: Logarithmic Functions And Their Graphs

Problem 137E

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Question

14. Solve the following:
(a) If graph G is self-complementary (see Problem 1):
(i) Determine |E| if |V | = n.
(ii) Prove that G is connected.
(b) Let n = 4k or n = 4k + 1 for a non-negative number k. Prove that there exists a self-
complementary graph G = (V, E) where |V | = n.

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