Strongly edge triangle regular graphs and a conjecture of Kotzig Original Research Article

The concepts of strongly vertex triangle regular graphs and strongly edge triangle regular graphs are introduced. An expression for the triangle number of a vertex in the composition of two graphs is obtained. It is proved that a self-complementary graph is strongly regular if and only if it is strongly edge triangle regular. Using these, we continue the analysis of a conjecture of Kotzig on self-complementary graphs.