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One - One function

An ordered n-...

Question

An ordered n-tuple $(d_{1}, d_{2}, . . ., d_{n}) with d_{1} \geq d_{2}, . . . \geq d_{n}$ is called graphic if there exists a simple undirected graph with n vertices having degree $d_{1}, d_{2}, . . ., d_{n}$ respectively. Which of the following 6-tuples is NOT graphic?

A

(1, 1, 1, 1, 1, 1)

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B

(2, 2, 2, 2, 2, 2)

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C

(3, 3, 3, 1, 0, 0)

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D

(3, 2, 1, 1, 1, 0)

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Solution

The correct option is C (3, 3, 3, 1, 0, 0)
Use the Havell-hakimi algorithm.
The sequence of steps in the algorithm for each graph is shown below:

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