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

 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.