Question 1(adsbygoogle = window.adsbygoogle || []).push({});

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"Prove that if (d_1, d_2, ... d_n) is a sequence of natural numbers whos sum is even (n>=1) then there is a pseudograph with n vertcies such that vertex i has degree d_i for all i=1,2,...n"

So we have a sequence of natural numbers... Something like this; we have a sequence... 1+2+3+4+5+6+7...+d_n, and their sum is even. So if we have d_n verticies, and are on the vertex i=n, then vertex i has degree d_i, which is d_n. And that's true for any i.

But I'm not sure if that's just restating the question...

Question 2

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Show that if graph G is not connected, then its complement is connected.

"In graph theory the complement or inverse of a graph G is a graph H on the same vertices such that two vertices of H are adjacent if and only if they are not adjacent in G. That is, to find the complement of a graph, you fill in all the missing edges, and remove all the edges that were already there. It is not the set complement of the graph; only the edges are complemented."

How do Ishowthis? I mean BY definition of completment, we see that the complement has to be connected, it's the inverse of G!

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# Homework Help: [Discrete Math] Pseudograph's

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