Diagonalized Cartesian products of S-prime graphs are S-prime. Hellmuth, M., Ostermeier, L., & Stadler, P. F Discrete Mathematics, 312(1):74--80, Elsevier, 2012.
bibtex   
@article{hellmuth2012diagonalized,
  title={Diagonalized Cartesian products of S-prime graphs are S-prime},
  author={Hellmuth, Marc and Ostermeier, Lydia and Stadler, Peter F},
  journal={Discrete Mathematics},
  volume={312},
  number={1},
  pages={74--80},
  year={2012},
  publisher={Elsevier}
}

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