## Self complementary cartesian products

### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

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?

-

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 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 at 6:00
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.920283854007721, "perplexity_flag": "head"}