(a) Determine the smallest positive value of n for which a simple graph on n vertices and 2n edges can exist. Give an example of such a graph for the smallest n. b) Let G be a simple graph with 20 vertices. Suppose that G has at most two com- ponents, and every pair of distinct vertices u and v satisfies the inequality that deg(u) + deg(v) > 19. Prove that G is connected.
(a) Determine the smallest positive value of n for which a simple graph on n vertices and 2n edges can exist. Give an example of such a graph for the smallest n. b) Let G be a simple graph with 20 vertices. Suppose that G has at most two com- ponents, and every pair of distinct vertices u and v satisfies the inequality that deg(u) + deg(v) > 19. Prove that G is connected.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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