Given two graphs $G$ and $H$ is there a nice way to check whether the cartesian product $G\Box H$ is self complementary without directly computing its complement and searching for isomorphism? For example, how can one show that $K_3\Box K_3$ is self complementary?
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$\begingroup$ This looks very much like a homework question. One could show $K_3\Box K_3$ was self complementary by a couple of drawings. $\endgroup$– Chris GodsilCommented Jan 21, 2013 at 12:56
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$\begingroup$ @Chris godsil: Yes, thats why I said without computing the complement, may be using some arguments on the degrees of verices and using the fact that it is a cartesian product; and this is not a homework. $\endgroup$– Pritam MajumderCommented Jan 22, 2013 at 6:00
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