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Finding self complementary graphs

  1. Jan 29, 2012 #1
    Suppose I let H and K be self complementary graphs where K has
    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?
  2. jcsd
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