On a Decomposition of Complete Graphs

Abstract.It is shown, among other results, that for any prime power q, the complete graph on 1+q+q2+q3 vertices can be decomposed into a union of 1+q Siamese Strongly Regular Graphs SRG(1+q+q2+q3,q+q2,q−1,q+1) sharing 1+q2 cliques of size 1+q.