6. (a) Determine the smallest positive value of n for which a simple graph on n vertices and 2n edges can exist. Give an

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6. (a) Determine the smallest positive value of n for which a simple graph on n vertices and 2n edges can exist. Give an

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6 A Determine The Smallest Positive Value Of N For Which A Simple Graph On N Vertices And 2n Edges Can Exist Give An 1
6 A Determine The Smallest Positive Value Of N For Which A Simple Graph On N Vertices And 2n Edges Can Exist Give An 1 (34.1 KiB) Viewed 30 times
6. (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() > 19. Prove that G is connected.
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