Show that every nonincreasing sequence of nonnegative

Chapter , Problem 47E

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Problem 47EShow that every nonincreasing sequence of nonnegative integers with an even sum of its terms is the degree sequence of a pseudograph. that is, an undirected graph where loops are allowed. [Hint: Construct such a graph by first adding as many loops as possible at each vertex. Then add additional edges connecting vertices of odd degree. Explain why this construction works.]

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