Decompositions of \(\lambda K_{n}\) into LEO and ELO Graphs

The authors previously defined the Stanton-type graph \(S(n,m)\) and demonstrated how to decompose \(\lambda K_n\) (for the appropriate minimal values of \(\lambda\)) into Stanton-type graphs \(S(4, 3)\) of the LOE-, OLE-, LEO-, and ELO-types. Sarvate and Zhang showed that for all possible values of \(\lambda\), the necessary conditions are sufficient for LOE- and OLE-decompositions. In this paper, we show that for all possible values of \(\lambda\), the necessary conditions are sufficient for LEO- and ELO-decompositions.