The number of open chains of length three and the parity of the number of open chains of length k in self-complementary graphs

In this paper it is shown, using the Sieve formula, that the number of open chains of length k, k ? 5, in a self-complementary (s.c.) graph is always even. As a corollary, it follows that the number of hamiltonian chains in a s.c. graph of order p > 5 is even, a result proved earlier by Camion. Further, the minimum number and the maximum number of open chains of length 3 in s.c. graphs of order p are determined, and the s.c. graphs of order p which attain these bounds are characterized.