# On the well-coveredness of Cartesian products of graphs

@article{Fradkin2009OnTW, title={On the well-coveredness of Cartesian products of graphs}, author={Alexandra Ovetsky Fradkin}, journal={Discrete Mathematics}, year={2009}, volume={309}, pages={238-246} }

- Published 2009 in Discrete Mathematics
DOI:10.1016/j.disc.2007.12.083

A graph G is well-covered if every maximal independent set has the same cardinality. This paper investigates when the Cartesian product of two graphs is well-covered. We prove that if G and H both belong to a large class of graphs that includes all non-wellcovered triangle-free graphs and most well-covered triangle-free graphs, then G × H is not well-covered. We also show that if G is not well-covered, then neither is G × G. Finally, we show that G × G is not well-covered for all graphs of… CONTINUE READING