Question: There is a connected graph with 8 vertices and 21 edges which has no HC since 21 = (n 1)(n 2)/2 + 1 for n

There is a connected graph with 8 vertices and 21 edges which has no HC since 21 = (n 1)(n 2)/2 + 1 for n = 8. Is there such a graph if we assume in addition that each vertex has degree at least 2? Please provide one if it exists, or provide the argument if such graph does not exist.

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