Suppose I let H and K be self complementary graphs where K has(adsbygoogle = window.adsbygoogle || []).push({});

an order that is even, say, m. And if I produce another graph

F from H and K by joining a vertex from K only when the vertex

is of degree less than m/2 to every vertex of H, then how

would this make F self complementary also?

If K has even order m and is self complementary, then its size

will be (m*(m-1))/4 but what can I say about H other than

it is also self complementary by hypothesis? and how can I use

the idea that any vertex in K of degree < m/2 is joined to

every vertex of H will lead to the construction of a self

complementary graph F?

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# Finding self complementary graphs

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