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Graph vertices

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1.2 Let n be a given positive integer, and let r and s be nonnegative integers such that r+s=n and s is even . Show that there exists a graph G of order n having r even vertices and s odd vertices.

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Solution Summary

This is a proof the existence of a graph with given vertices.

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Either r is even or r is odd. Consider the two cases separately. (S is always even)

a) r is odd

Form a graph that consists of two components: the complete subgraph on r vertices and the complete ...

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