Decompositions of $\lambda K_n$ into LEO and ELO Graphs

Abstract

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.