Abstract:

In order to construct Steiner triple systems of order t^2，the basic concept of constructing Steiner trlple systems of orbitrary order  is described,and the definition of edges matrix of a complete graph is given.A method of constructing Steiner triple systems of order t² is proposed. The entire procedure of constructing Kirkman triple systems of order 9 is presented. Practice shows that the concept of constructing Steiner triple systems of order t² is correct,it is worth to promote,edges mctrix as a new tool in graph theory study.

Key words: steiner triple systems, construction, complete graph, edges matrix, order