The Spectra for Two Classes of Graph Designs

Abstract

A $(\lambda K_n,G)$-design is a partition of the edges of $\lambda K_n$, into sub-graphs each of which is isomorphic to $G$. In this paper, we investigate the existence of $(K_n,G_{16})$-design and $(K_n,G_{20})$-design, and prove that the necessary conditions for the existence of the two classes of graph designs are also sufficient.