Non-isomorphic non-hamiltonian graphs

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I have the following question:

Find an infinite family of non-isomorphic graphs without hamiltonian paths such that $\delta(u) + \delta(v) \geq |V(G)| - 2$ for every non adjacent vertices $u, v$.

I'm new in these topics, so I don't know where to start. Can somebody give me a hint or some help with this?

Thanks in advance!