Abstract: Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k+1, where 4k+1=x2+y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k+1 orders.

Key words: strongly regular self-complementary graphs;strongly edge triangle regular, eigenvalues;circular graphs