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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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This looks very much like a homework question. One could show $K_3\Box K_3$ was self complementary by a couple of drawings. –  Chris Godsil Jan 21 '13 at 12:56
    
@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. –  pritam Jan 22 '13 at 6:00

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